OB 44 
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He Mathematics 
of the Sky 




By 

CHAS, J. BURTON 




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THE BIBLE AND THE TELESCOPE 

A popular Astronomical Journal, 

CHAS. J. BURTON, Editor. 
Quarterly — 80c a year. 

Address: 

CHAS. J. BURTON, 

1501-1 509 University Ave. S. E., 

Minneapolis, Minn. 



The 

Mathematics 
of the Sky 



OR 



The Stupendous Grasp of 

Figures as Applied to the 

Heavenly Bodies 



By 

CHAS /. BURTON, 

Ph.D., D.D. LL.D. 
Professor of Astronomy and the Bible, 
in the International Christian College, 

Minneapolis, Minn. 



STANDARD PRESS 
1920 






Copyright secured 1920 
By C. J. Burton 



THE RING NEBULA IN LYRA 




A very few ring Nebulas are known, 
of which the one in Lyra is the finest. 
It has a very faint star of the fifteenth 
magnitude near its center. It was dis 
covered by Darquier in 1779, while fol- 
lowing Bode's comet of that year. It 
is located about 10 degrees Southeast 
of the bright star Vega. 



JAN -3 1321 
©CU605201 



PREFACE 

Reveling in the depths of space, 
reflecting on the grandeur of the uni- 
verse and calculating on the vastness 
of its dimensions have brought many 
delightful hours while preparing the 
material for this book. 

It is not a dry and prosy collection 
of numbers brought together for the 
sake of looking at them, but the study 
of the heavens which is back of the 
book fires the imagination and stirs 
the soul to grander conceptions of the 
magnificence of the universe, and to 
nobler aspirations and reverence for 
the God who made it. May every 
hour spent in reading this book fill 
the mind of the reader with more 
reverent thoughts concerning Him who 
created all things. 

In locating various stars, clusters 
and nebulas I have generally spelled 
out the words degrees and minutes, 
because the signs for degrees and 
minutes of an arc are not ordinarily 
supplied by the linotype. 

CHAS J. BURTON. 

Minneapolis, Minn., May 1, 1920. 



6 THE MATHEMATICS 

PRELIMINARY THOUGHTS 

"Science interpreted is theology." 

"Deity works by methods and means." 

"Science prosecuted to its conclusion^ 
leads to God." 

"The elucidation oi the great problems 
of philosophic or speculative theology 
ifc, indeed, the highest function of 
science." 

"It is not for its facts, but for the 
significance of the facts, that science is 
valuable." 

"To accumulate the data of science 
is good; to interpret them is the 
noblest prerogative of a thinking be- 
ing." 

"All our learning would in reality 
be but the "vanity* which it is some- 
times reproached with being if it could 
reflect no light upon the origin, the 
nature, the duty, and the destiny of 
man." — Winchell. 



NATURE A REVELATION 

We cannot resist the conviction that 
Nature is intended as a revelation of 
God to all intelligences. If it be so 
intended, Nature must be capable of 
fulfilling the offices of a revelation, 
and a knowledge of her phenomena 
and laws must afford the data of a 
theology. 



OF THE SKY 7 

Despite the skepticism of a certain 
school of recent writers, the pheno- 
mena of the universe continue to in- 
spire in the soul ot man emotions of 
religious reverence and worship. To 
the mass of mind, as to the intelligence 
of Socrates, and Plato, and Kepler, 
and Newton, and Galen, and Paley, 
and Buckland, the order or the Cosmos 
proclaims an infinite intelligence. — 
Winchell. 



"Lift up your eyes on high, and be- 
hold who hath created these things, 
that brought out their host by number : 
He calleth them all by names by the 
greatness of His might, for that He 
is Strong in power, not one faileth. v 
Isa. 40:26. 



"Is not God in the height of heaven? 
and behold the height of the stars, how 
high they are ! And thou sayest, how 
doth God know? Can He judge 
through the dark cloud? thick clouds 
are a covering to him, that he seeth 
not; and He walketh in the circuit of 
heaven." Job 22:12-14. 



DONATI'S COMET 

This comet which appeared in 1858 
was a subject of universal wonder. Its 



8 THE MATHEMATICS 

tail was 50,000,000 miles in length, and 
its head was 250,000 miles in diameter. 
It parsed over the first magnitude star, 
Arcturus, Oct. 5, 1858, and came near- 
est the earth on Oct. 10 of the same 
year. It remained visible for more 
than 9 months, and will not appear 
again for nearly 2,000 years. 



THE TELESCOPE AND JUPITER'S 
FAMILY 

Not until June 7, 1610 was it known 
that Jupiter had any moons. Galileo 
found the 4 larger ones on that memo- 
rable night with his 30-inch "Optic 
Tube." A new era was then opened 
in astronomy. These 4 moons are 
known by the mythological names of 
Io, Europa, Ganymede, and Callisto. 
During nearly 300 years from Galileo's 
triumph to the Lick Refractor these 
4 moons of Jupiter were supposed to 
be the full number, but a fifth satellite 
was added by E. E. Barnard at Mt. 
Hamilton in Sept., 1892. It has a 
period of 11 hours and 57 minutes and 
is 112,500 miles from the planet. Two 
additional moons were added to 
Jupiter's system in Dec. 1904 and Jan. 
1905 by Prof. Perrine of the Lick Ob- 
servatory. Finally on Feb. 28, 1908, 
P. Melotte of Greenwich Observatory, 



OF THE SKY 9 

found an eighth moon of Jupiter. Its 
movement is retrograde, which anomaly 
is of va'st cosmical importance. 



A TELESCOPE ON THE NEAREST 
STAR TO US 

If you could stand on Alpha Cen- 
tauri, the nearest star to the solar sys- 
tem, (4% light years away), and look 
at our sun, it would appear no brighter 
than Polaris does to us, "so great is its 
distance, and you could not see a 
single one of our planets even if you 
should look through Lord Rosse's great 
60-foot telescope, which is 6 feet in 
diameter. 



The Mathematics of the 
Sky 

CHAPTER ONE 
THE TELESCOPE AND THE 
UNIVERSE 
1. The Telescope. 
While "the eye is not satisfied with 
seeing," (Eccl. 1:8), the telescope in- 
vented three hundred years ago ha$ 
come to assist the eye, and now enables 
it to look out into space and bring to 
view millions of suns that are known 
to be hundreds of light years from the 
solar system. 



10 THE MATHEMATICS 

This instrument has given man a 
broader view of the bigness and mag- 
nificence of the Universe. The human 
eye unaided can see distinctly not more 
than seven thousand stars, but if one 
should look through one of the greaf 
telescopes, he would be astonished to 
find at lea^t a hundred millions of 
luminous suns in space. Sir William 
Herschel calculated that his twenty- 
foot reflector would penetrate into 
space and reach stars that are nine 
hundred times the distance of Sirius, 
and that his forty-foot reflector would 
bring to view stars that are twenty- 
eight hundred time's the same distance. 
This is vast, simply enormous. Mr. 
Herschers forty- foot reflector, with an 
object glass of 48 inches, showed stars 
up to the eighteenth magnitude of our 
present day classifications. Sirius is 
known to be more than fifty trillions 
of miles from us, which means that it 
is eight and a half light years from 
the Solar System. 

While the Yerkes and Lick telescopes 
have magnifying powers of more than 
three thousand diameters, Such instru- 
ments being intended to study the 
heavenly bodies in detail, the glasses 
that give the best satisfaction to the 
average person are of comparatively 



OF THE SKY ll 

moderate magnifying power, say about 
two hundred to three hundred diame- 
ters. 

No minister, or other educated per- 
son, can afford to omit from his cur- 
riculum of study God's great Book of 
Nature. It should accompany the study 
of Revelation, the Holy Scriptures. 

As we look out upon God's great 
universe and behold the beauty, the 
grandeur and the magnificence of His 
works, either with the naked eye or 
by the help of the telescope, we are 
constrained to Say in the language of 
the Psalmist, "O Lord, how manifold 
are Thy works! In wisdom hast Thou 
made them all; the earth is full of 
Thy riches." Psa. 104:24. 
2. The Universe. 

From the Latin Universum. Unus 
one and vertere to turn, that is, turned 
into one, combined into one whole; all 
created things viewed as one system. 

I. What? 
1. Stars or Suns. 

(1) Luminous ones. The tele- 
scope finds at least 100,000,- 
000. 

(a) First magnitude start, 20 
in all. 

(b) Double stars, at least 12,- 



12 THE MATHEMATICS 

000 couples have been found. 
Also many triples and 
quadruples. 

(c) Variable stars. 

(d) Temporary stars. 

(e) The solar system, com- 
posed of the sun and 8 
larger planets, 26 moons, 
and near 600 asteroids, also 
meteors and comets. 

(2) Opaque. Probably millions 
of these also. 

2. Nebulae. Ten thousand have 
been catalogued. Estimated to 
be at least one hundred and 
twenty thousand of them in the 
heavens. The most prominent 
are: 

(1) The Great Nebula in Orion. 

(2) Ring Nebula in Lyra. 

(3) The Trifid Nebula. 

(4) Dumb-bell Nebula. 

(5) Great Spiral Nebula. 

(6) Great Nebula in Andromeda. 

3. Star Clusters. Most noted are, 

(1) The Pleiades. 

(2) The Hyades. 

(3) The Praesepe. 

(4) Great cluster in Hercules. 

4. Comets. Many millions of these, 
some invisible to the naked eye, 



OF THE SKY 13 

some few very bright and strik- 
ing. 

They are divided into short 
period and long period comets 
and those that never return to 
the solar system after one visit. 

II. Extent f Known only to the 
Creator, but it is known to be 
vast. Sir Wm. HerSchel cal- 
culated that his 40-foot reflector 
reaches stars 2800 times the dist- 
ance of Sirius, and this star is 
known to be fifty trillions of 
miles from the solar system, or 
eight and one-half light years' 
away from us. 

III. How and When? "In the be- 
ginning God created the heavens 
and the earth." Gen. 1:1. Hence 
the universe did not come by 
chance, and it is not eternal. 



CHAPTER TWO 
STUDIES IN CELESTIAL ARITH- 
METIC 
1. The Moon. Our nearest neighbor, 
and the most interesting object in 
the sky to people on the earth, except 
the sun. 

(1) Its diameter is 2163 miles; its 
volume is about 1/50 that of the earth 



14 THE MATHEMATICS 

while in mass it would take 81 moon's 
to make an earth. The pull of gravity 
on its surface is only 1/6 of what it is 
on the earth. Its sidereal revolution 
covers about 27% days, while its sy- 
nodic period is about 29% days. 

(2) It turns on its axis once while 
traveling around the earth and hence 
keeps the same face towards u's con- 
tinually. 

(3) Its average distance from the 
earth is about 240,000 miles, and an ex- 
press train traveling at 60 miles per 
hour could go to the moon and back 
in 11 months. A round trip ticket at 
3c a mile would cost $14,400. 

(4) One of the highest mountains 
on the moon is called Leibnitz, and is 
fully 6 miles high. The Surface of the 
moon contains several thousand craters 
and some of these are from 14 to 100 
miles across. Copernicus, one of its 
great craters, is fully 13,000 feet high. 
The mountains of the moon are much 
higher in proportion than those upon 
the earth. 

(5) The moon in its revolution 
around the earth travels at the rate of 
3355 feet per second, 38 miles per 
minute, 2288 milts per hour, and com- 
pletes a revolution around the earth in 
27% days. It travels from west to 



OF THE SKY 15 

east and covers about 13° on the face 
of the sky daily. It would take more 
than 600,000 full moorts to equal the 
light of the sun as its shines upon the 
earth. 

(6) If a person should stand on the 
moon and look at the earth, it would 
look 14 times a's large as the moon 
looks to us upon the earth. While it 
takes nearly 50 moons in volume to 
equal the earth, it takes more than 60,- 
000,000 moons to equal the sun. While 
it takes 81 moon's to weigh as much 
as the earth, it takes 26,892,000 moons 
to weigh as much as the sun. 

2. The Sun. To us he i*s the most 
magnificent of all the heavenly bodies. 

(1) His distance is 93,000,000 miles 
from the earth. A passenger train 
running 30 mile's per hour would re- 
quire 352 years to make a journey to 
the sun, and a round trip ticket at 3c 
a mile would cost $5,580,000. Preach- 
ers traveling at half fare would have 
to pay $2,790,000. A cannon ball travel- 
ing at 1760 feet per second would re- 
quire nearly 9 years to reach the sun. 

(2) The sun and moon appear about 
the Same size, but if the sun could be 
brought as near the earth as the moon, 
it would seem to us as large as 160,000 
moons, resulting in practically no night, 



16 THE MATHEMATICS 

for it would fill the whole heavens. 
Furthemore, the earth would be 160,000 
times as hot as it is now, and nothing 
could live upon it tor a moment. 

(3) The amount of light and heat 
given off by the sun has been cal- 
culated. The annual amount of heat 
received by the earth is sufficient to 
melt a layer of ice over its entire sur- 
face 114 feet thick; but the amount 
the earth receives must be multiplied 
by 2,170,000,000 to get the whole 
amount of solar radiation for the same 
time — one year. 

(4) The sun is 750 times greater than 
all the planets combined — , the 8 larger 
planets, nearly 600 asteroids and 26 
moons. If we should represent the 
earth by a marble one inch in diameter, 
the sun would be represented by a 
ball nine feet in diameter, and on this 
scale the earth would be 968 feet from 
the sun. On the same 'scale, Neptune 
would be Sy 2 miles away, and the 
nearest star would be 49,500 miles 
distant, while Polaris would be at least 
495,000 mile's away. 

(5) To get a better idea of the vast 
volume of the sun, remember that it 
is 866,000 mile's in diameter which is 
109 times that of the earth's diameter; 
its surface is 12,000 times that of the 



OF THE SKY 17 

earth; while its volume is 1,300,000 
times that of the earth. Its mass is 
332,000 time* that of the earth. While 
its density is only one-fourth as much 
as the earth's, its superficial gravity is 
27.6 time's greater than that of the 
earth. In other words a body weigh- 
ing 100 pounds on the earth would 
weigh 2760 pounds if carried to the 
surface of the sun. If an aeroplane 
could circle the earth in 10 days it 
would require 3 years for it to circle 
the sun. 

If the earth were as large as the 
sun, and all objects on the earth were 
correspondingly as large, a man 6 feet 
tall would be increased to one-eighth of 
a mile; his arms from his Shoulders 
to the tips of his fingers would be 
more than 160 feet long ; his legs would 
be more than 250 feet long; his eyeS 
would be 9 feet in diameter, while 
his nose would be about 14 feet long. 
The Mississippi River would be 140,000 
miles long, and at Memphis, Tenn., it 
would be 109 mile's across; Pike's Peak 
would be 292 miles high, while mount 
Everest would be over 500 miles above 
sea level. The Atlantic Ocean would 
be 327,000 miles wide, and from one 
side of Chicago to the other would be 



18 THE MATHEMATICS 

more than 2000 miles. A train of cars 
containing 10 coaches would be more 
than 8 miles long. 



CHAPTER THREE 

THE BIGNESS OF THE SOLAR 

SYSTEM 

The Ptolemaic system of astronomy 
gave way about the time of the dis- 
covery of the new world by Columbus. 
The Copernican system then came into 
popular favor. It was shown and 
proved that the diurnal movement of 
the heavens was due to the rotation 
of the earth on its axis. Real and 
apparent motion were pointed out and 
explained by Copernicus. The earth 
was given its true position in the 
universe, with the sun as the center of 
the solar System. A family of 8 larger 
planets and nearly 600 asteroids have 
been found to revolve around the sun 
in regular times and at definite distan- 
ces. 

But before the year 1781 it was not 
known that there were any planets be- 
yond the orbit of Saturn. While the 
first real telescope was invented and 
used by Galileo in 1610, no new planet 
was discovered till 171 years later when 
Uranus was discovered in 1781 A. D. 
by the great astronomer Herschel. It 



OF THE SKY 19 

was found by accident and with a rela- 
tively small telescope of 7-foot length. 
This leads me to say that small tele- 
scopes have been used in the past and 
may be used in the future in making 
important discoveries. The instrument 
that found the 4 larger moons of 
Jupiter was a 30-inch instrument. Do 
not despise the small glass. Secure 
one for your own use if possible and 
use it indujtriou'sly and enthusiastically. 
It will repay you many times in both 
pleasure and profit. 

But I am digressing. Let us get 
back to Herschel and the planet 
Uranus. Anciently and up till 1781, 
Saturn was considered the outside 
planet of the solar system. This planet 
revolves around the sun at a distance 
of 886,000,000 miles from him. Double 
these figure's and you have the dimen- 
sions of the solar system as known at 
that time. It will be 1,772,000,000 miles 
and represents the diameter of Saturn's 
orbit. But an hour or two before mid- 
night of March 13, 1781 the solar sys- 
tem was suddenly doubled, and Wm. 
Herschel was suddenly made famous. 
His small telescope had done the work. 
He was industriously looking for other 
objects, searching among some stars 
in the constellation of Gemini when 



20 THE MATHEMATICS 

the discovery was made. The dimen- 
sions of the solar system were thus 
doubled, for Uranus' orbit was found 
to be about double that of Saturn's, 
1,800,000,000 miles from the sun. This 
was a great triumph and created much 
attention and excitement among tstron- 
omers. The study of astronomy be- 
came popular, telescopes were in de- 
mand and everybody wanted one. 

Thus Wm. Herschel was brought 
out of obscurity into universal popular- 
ity and renown. Not only so, but he 
was lifted from poverty and incon- 
venience into favor and influence in 
many ways. Remember that Herschel 
by industry and perseverance became 
one of the world's greatest astronom- 
ers in the face of seemingly insur- 
mountable obstacles. He was without 
a university education, but he made 
up for this by diligence, hard work, 
enthusiasm and a perseverance that 
conquered all difficulties. He learned 
to grind lenses and build telescopes, 
and after the discovery of Uranus the 
king gave him the means to build his 
great 40-ft. reflector. This was the 
crowning work of his life, for with 
it he penetrated into space and found 
stars of the 18th magnitude and so far 
away that it take's their light thousands 



OF THE SKY 21 

of years to reach the human eye. He 
became a Fellow of the Royal Society, 
was given an observatory by the king 
and received a salary of $1000 a year, 
which was quite respectable in those 
days. But back to Uranus again. 
This planet is just about at the limits 
of visibility to the unaided eye. 
though it is 32,000 miles in diameter 
and fully 64 times as large as the 
earth. It makes a journey around the 
sun in nearly 84 years traveling at the 
rate of 4% miles per second. A child 
is born, it passes its youth into 
young manhood, then into married life, 
middle life, old age and dies at the 
age of 84 while Uranus makes one 
revolution around the sun. But it is 
never tired. It goes on and on and on. 

The planet Uranus is so far away 
from the earth at its nearest approch 
that a limited fast-line expres's train 
running 1000 miles a day would require 
more than 4600 years to span the 
distance. 

But 65 years after the discovery of 
Uranus, the diameter of the Solar 
system was extended 2,000,000,000 miles. 
On Sept. 23, 1846 the planet Neptune 
was discovered. It was not found by 
accident a's Uranus had been, but its 
discovery came about because two men 



22 THE MATHEMATICS 

searched for it and calculated its place 
in the heavens, though the planet was 
invisible. One of these men wa5 
Leverrier of France, the other was 
Adams, an English astronomer. These 
men spent nearly two years making 
their drawings and calculations to find 
the place in the sky where the planet 
was believed to be. It is remarkable 
that neither of these men knew that 
the other was making calculations to 
find an unknown planet. But the result 
of their calculation's almost agreed. 
These men did not, and could not, 
know that there was another planet 
farther out than Uranus, by means of 
their natural eyes; but they did know 
or 'strongly believed through their 
mathematical eyes that there was such 
a planet. Hence their search by means 
of two years of laborious calculations. 
It wa's the behavior of Uranus that 
led them to believe there was another 
planet outside his orbit. They could 
see an invisible body pulling on Ura- 
nus, disturbing him in his journey 
around the fcun, hastening him or 
holding him back in certain portions 
of his orbit. They therefore prepared 
to find the unknown body. After the 
drawings and calculations were all com- 
pleted, Leverrier requested the astron- 



OF THE SKY 23 

omer Galle to direct the telescope to a 
certain point in the constellation of 
Aquarius, and he would find the un- 
known body. It wa's found within 
a half hour and within less than a 
degree of the place where Leverrier 
said it would be. This discovery is 
regarded as one of the greatest mathe- 
matical achievements of the human 
mind. Such feats as this strengthen 
and confirm our faith in the mathema- 
tics of the heavens. And now since 
Neptune has been found, what are the 
great mathematical le k ssons forced upon 
our minds? This brings the dimen- 
sions of the solar system to twice the 
distance of Neptune from the sun. 
Neptune's distance being 2,800,000,000 
miles from the sun, the diameter of 
his orbit is 5,600,000,000 miles. He 
circles the 'sun in nearly 165 years, and 
travels in an orbit 3-1/7 times the dia- 
meter of his orbit, at the rate of 3% 
miles per second. His distance from 
the Sun is so vast that the light of the 
sun requires 4 hours and 10 minutes to 
reach Neptune. Now remember that 
light travels through space at the in- 
conceivable rate of 186,000 miles per 
second. 

In order to get perhaps a clearer idea 
of the meaning of this distance, con- 



24 THE MATHEMATICS 

sider the following illustration. Sound 
travels through the air at the rate of 
1090 feet per second. Suppose there 
is an explosion on the sun, and sup- 
pose that the sound of this explosion 
could be carried through space at the 
same rate of 1090 per second till it 
reached the planet Neptune. It would 
require more than 430 years for the 
report of the explosion to be heard on 
Neptune. 

Another illustration. Suppose that 
aeroplanes were used away back in Old 
Testament times, and one of these 
machines actually started from the 
earth to the planet Neptune via the 
intervening planets — , Mars, Jupiter, 
Saturn, and Uranus, passing them in 
regular order, but never making a 
stop at any one of them. Suppose the 
machine started from the earth in the 
days of Judges, in 1170 B. C, near the 
time of Jephthah, the 9th judge, 
(Judges 11th chap.), and traveled all 
the way at 100 miles per hour, or 2400 
miles per day. The first part of the 
journey was from the earth to Mars, 
a distance of 48,500,000 miles when that 
planet is nearest the earth. It required 
55 years and passed the planet Mars, 
therefore, in 1115 B. C, within a few 
years of the death of Samson. The 



OF THE SKY 25 

Second part of the journey was from 
Mars to the planet Jupiter, a distance 
of 342,000,000 miles. This paffof 
the journey required 390 years and it 
passed Jupiter in 725 B. C, four years 
before Shalmanezer carried the ten 
tribes into captivity. The third part 
of the journey was from Jupiter to 
the planet Saturn, a distanve of 403, 
000,000 miles. It required 460 years 
and passed Saturn in 265 B. C. within 
a few years of the date when the 
Septuagint version of the Old Testa- 
ment was made. The fourth part of 
the journey was from Saturn to the 
planet Uranus, a distance of 914,000,000 
miles. The time required was 1043 
years and it pas'sed Uranus in 778 
A. D., the year in which Charlemagne 
made an invasion of Spain and an- 
nexed the country between the Ebro 
and the Pyrenees under the name of 
the "Spanish March." The fifth part of 
the journey was from Uranus to the 
planet Neptune, a distance of 1,000,000,- 
000 miles. It required 1142 years and 
arrived on the planet Neptune in A. D. 
1920, this present year of grace. In 
other words, the distance from the 
earth to Neptune (2,707,000,000 miles) 
is so vast that the aeroplane which 
Started from the earth to Neptune in 



26 THE MATHEMATICS 

the year B. G. 1170, traveling con- 
stantly night and day at the rate of 100 
miles per hour, finished the excursion 
at the completion of 3090 years, ar- 
riving on Neptune in 1920 A. D. 



CHAPTER FOUR 
WEIGHT OF THE SUN AND 

PLANETS 
The amount of matter in each planet 
and moon of the solar system as well 
as that of the sun himself has been 
calculated. In other words, each one 
of these bodies has been weighed. And 
this is one of the most wonderful 
achievements that astronomer's have 
been able to accomplish. The problem 
of finding their weight, or of finding 
the amount of matter in each, is really 
a very difficult task. Yet the problem 
has been solved and the principle on 
which it has been done is as simple as 
that which has been used in finding 
their dimensions. The following figures 
express the weight of the earth in 
tons: 6,000,000,000,000,000,000,000, or six 
sextillion tons. Of course these figures 
are meaningless to us because the mind 
cannot grasp so stupendous a number, 
yet they represent the amout of matter 
which the earth contains. To find the 
weight of the sun, multiply the earth's 



OF THE SKY 27 

weight by 332,000, because the sun con- 
tains 332,000 times as much material 
as the earth. 

Comparing the sun with the other 
planets we have the following: It 
takes 27,000,000 moons to weigh as 
much as the sun; 7,000,000 Mercuries; 
407,000 worlds like Venus to equal 
the weight of the sun; 3,000,000 bodies 
like Mars ; 1048 Jupiters ; 3502 Saturns ; 
22,760 worlds like Uranus; and 19,500 
Neptunes to weigh as much as the 'sun. 

Comparing the earth with the other 
planets we have the following: It 
takes nearly 82 moons to equal the 
earth in weight; 21 Mercuries; Venus 
weighs 8/10 as mucn as the earth; it 
takes 9 worlds like Mars to weigh as? 
much as the earth ; it takes 317 earth's 
to weight as much as Jupiter; 95 
earths to weigh as much as Saturn; 
14% earths to equal Uranus in weight; 
and 17 earth's to weigh as much as 
Neptune. 

Now remember as has been stated 
before that the sun is 750 times as 
great as all the planets and moons of 
the solar system combined. Is it any 
wonder, then, that the sun has such 
tremendous pulling power, holding all 
the planets in their orbits and com- 
pelling them to revolve around him? 



28 THE MATHEMATICS 

Is it any wonder hat he has the 
power to reach out and take hold of 
far-away Neptune, 2,800,000,000 miles 
distant, and say to him, you may con- 
tinue to travel around me, but you 
shall not get any further away? Re- 
member, that while Neptune fa 32,000 
miles in diameter, it takes 19,500 
Neptunes to weigh as much as the 
sun. But this is not all. The sun's 
power of attraction does not stop with 
Neptune. There are a number of 
comets that go out into space hundreds 
of times' the distance of Neptune, and 
in every part of their journey they are 
under the influence and power of the 
sun's attraction. They go on journeys 
of hundreds or even thousands of 
years, but they are compelled by the 
superiority of the sun to return. 



CHAPTER FIVE 
ALPHA CENTAURI AND ITS 

MATHEMATICAL LESSONS 
The four preceding chapters have 
been devoted mainly to the sun and his 
family, and we have been led to get a 
view of the vast dimensions of our 
!solar system, expressed by the awiful 
grasp of figures that tell us of its 
boundary. While the outer planet of 
this system is at the inconceivable 



OF THE SKY 29 

distance of 2,800,000,000 miles from the 
sun this distance is but a step, a 
mile, a measuring unit so to speak as 
compared with the vastness of the 
great void separating us from the near- 
est fixed star. When we have covered 
the space from the sun to the orbit of 
Neptune, we have just arrived at the 
front gate of our own premises, getting 
ready to start toward Alpha Centauri. 
This is a first magnitude star in the 
southern heavens and cannot be seen 
in this country except in the southern 
portion of the Gulf states. It is situat- 
ed in right ascension 14 hrs. 32 mi., 
and 60d 25m southern Declination. It is 
a double star, and its components re- 
volve around their common center of 
gravity at a mean distance of almost 
25 times the radius of the earth's orbit, 
or 2,325,000,000 miles. The period of 
this binary system is 81 years. It is a 
great light-giving sun, and believed to 
be a little larger than our own sun. 
At any rate it is fully equal to it in 
luminuosity. 

But what can be said of the enor- 
mous distance of Alpha Centauri from 
us? How are we to get any idea of 
what is meant by 25,500,000,000,000 
miles? This distance is so vast that 
light traveling through space at the 



30 THE MATHEMATICS 

rate of 186,000 miles per second would 
require 4% years to span it. But this 
does not satisfy us and we must try 
another illustration. This star is 9000 
time the distance of Neptune from us, 
and we found in a preceding chapter 
that an aeroplane traveling at 100 miles 
per hour would spend 3090 years in 
going from the earth to the planet 
Neptune. We must therefore, multiply 
3090 by 9000 in order to find how long 
it would take the aeroplane to travel 
from the earth to Alpha Centauri. 
You will probably be asstonished to 
find by calculation that the time will 
be 27,810,000 years. Let us try another. 
We consider that sound is traveling at 
a rapid rate when it covers 1090 feet 
in a second of time, but at this rate 
if sound could be carried through 
space, it would require more than 
3,000,000 years to travel from the earth 
to Alpha Centauri. 

Here is another illustration. The 
Alpha star in the Centaur is in motion 
traveling through space at 14 miles per 
second. Let us suppose it is coming 
towards us at that rate, and will con- 
tinue to come in this direction till it 
reaches the solar system. How long 
will it take? Dividing the distance to 
Alpha star by 14, the result will be 



OF THE SKY 31 

seconds; divide this by 60 and the re- 
sult will be minutes; divide this by 
60 and the result will be hours; divide 
this by 24 and the result will be days; 
divide this by 365 and the result will 
be years. You will find that it will 
require more than 57,000 years for the 
star to reach this part of the universe. 
Still another illustration. Suppose a. 
passenger train starts from the earth 
to Alpha Centauri, traveling continually 
and making 1 mile per minute. How 
long will at take to reach the star? 
By performing the calculation you will 
find that 48,200,000 years will be re- 
quired. Now suppose that a ticket on 
this excursion one way costs lc per 
mile, what will be the fare to the star? 
The fare will be $255,000,000,000, as 
much as the great world war cost dur- 
ing the 4 years and 3 months it was 
running. Suppose the money for this 
ticket was put into standard silver dol- 
lars and piled one upon another, how 
far above the surface of the earth 
would the top dollar be? as it takes 
nine silver dollars to make an inch 
divide by 9 and reduce the inches to 
miles. The dollar on top of the 
column would be 445,000 miles high. It 
would reach to the moon and 207,000 
miles beyond. It would make a string 



32 THE MATHEMATICS 

of dollars all around the world 18 
times, these dollars hugging each 
other as closely as it is possible for 
them to be. 



CHAPTER SIX 
ANOTHER LESSON IN STAR 

DISTANCES 
It was not until 1838, that the dis- 
tance to a single star was known. 
Astronomers had been for year's trying 
to solve the problem. But in that year 
the distance to 61 Cygni was found to 
be about 8 light years from the solar 
system. It wa's the first star whose 
distance was measured. This star is 
found in the constellation of Cygnu's, 
in Right Ascension 21 hr. 2 m. and 38d 
15m Northern Declination. It is a 
few degrees southeast from the first 
magnitude star Derieb, and about 36d 
due ea'st from Vega, a first magnitude 
star in Lyra. It is also about 40d 
northeast from Altair in the constella- 
tion of Aquila. Only two stars are 
known to be closer to the sun than 61 
Cygni, and its distance is nearly 48,- 
000,000,000,000 miles. If you should 
attempt to count 48 trillions at the 
rate of 1 every second, and should 
succeed in the attempt, you would 
have to live more than 1,500,000 years, 



OF THE SKY 3 3 

counting day and night. You would 
have no time to eat or sleep, but 
would be compelled to put in every 
moment of your time counting, if you 
finished the job in the above men- 
tioned time. While this star is among 
the nearest to us, there is another one 
without a name of its own, but known 
as Lalande 21,185 that is a little nearer. 
It is a little under 7 light years away. 
The French astronomer Lalande num- 
bered it 21,185 in his catalogue of 
stars. This explains w T hy it is so 
called. It is located in Right Ascension 
10 hr. 58 m. and J6d 38m Northern 
Declination. This leads us to say that 
there are about 800,000 different stars 
appearing in the various catalogues of 
stars now published. So that every 
star found with a 3-inch telescope can 
be observed and indentified, excepting 
of course those in the Milky Way. 

The astronomer Lalande as men- 
tioned above contributed greatly to 
the general progress of astronomical 
science and in 1895 was appointed 
Director of the Paris Observatory. He 
published an important work entitled, 
"Treatise on Astronomy." 



34 THE MATHEMATICS 

CHAPTER SEVEN 
THE UNFIXEDNESS OF THE 

FIXED STARS 
Evidences of change are everywhere. 
Nothing is at rest. In the whole 
universe consisting of million's of stars, 
planets, comets, etc., there is not a 
single really fixed object. The term 
"fixed 'star" is only a paradox, and 
the stars appear to be fixed because of 
their enormous remoteness and the 
shortness of time in which we can 
observe them. The longest life of 
man is so short that to the untrained 
eye, the 'stars have seemed not to 
change. The fact is the star's are at 
such vast distances, that during a 
thousand years they would not have 
seemed to change their relative posi- 
tions. But modern astronomical in- 
struments prove that they are in mo- 
tion. Halley an English astronomer 
discovered early in the eighteenth cen- 
tury that both Arcturus and Siriu's 
have changed their positions in the 
sky during a few hundred years 
previous to that time, having moved 
in a southerly direction, Arcturus 
about one degree and Sirius a half 
degree. It i k s known that Arcturus is 
one of the large bodies in the uni- 
verse, many times larger than the sun; 



OF THE SKY 3 5 

that it is speeding through space at a 
frightful rate, prabably 200 miles or 
more per second; and yet it would 
take 800 years for it to pass over a 
space on the face of the sky equal to 
the diameter of the moon. How vast 
then must be its distance from us ! 

You will also find that the planets 
"seem to be fixed if you observe them 
only one night, and those farthest out 
from the sun do not seem to change 
their positions except after many ob- 
servations have been taken. For exam- 
ple, the planet Neptune moves eastward 
but little more than 2 degrees during 
a whole year. 

In course of time the beautiful con- 
stellations that now adorn the sky will 
be pulled apart; the "Bands of Orion 
will be loosed" ; the symmetrical big 
dipper will be torn to pieces ; and the 
whole face of the sky will be changed. 
Time will bring this about, and it is 
sure to come. These changes are all 
so many evidences of life and activity 
in every part of the universe, and ot 
the influence of the law of gravity by 
which the Creator is upholding and 
governing it. 



36 THE MATHEMATICS 

CHAPTER EIGHT 
THE SUN AND HIS FAMILY 

MIGRATING 
Not only are the stars, planets and 
comets moving rapidly through space, 
but our own sun is in actual motion, 
speeding along with a velocity forty 
times a k s great as that of the swiftest 
cannon ball. Sometimes people reflect- 
ing on this are constrained to ask the 
question: "If this is true, are we not 
in great danger of running up against 
another great Sun or a planet, or a 
comet, or some other* object som- 
where in space?" This leads me to 
say that our own sun and his attend- 
ants occupy a va'st field, surrounded by 
a great void containing only meteors, 
bolides and comets. A large number 
of comets belong to, and are a part of, 
the solar system. That is to 'say, they 
are physically connected with the sun, 
and no difference how far they may 
recede from him they will be compelled 
to return into perihelion after a period 
of hundreds or even thousands of 
year's. But there are also doubtless 
a number of comets that visit us once, 
and then go away never to return. But 
it is generally believed by astronomers, 
and there seem to be many evidences 
of the fact, that there are no large 



OF THE SKY 3 7 

bodies nearer to us than the great 
Alpha star in the Centaur, to which I 
called your attention in a previous 
chapter. This star is at least 277,000 
times as far from us as we are from 
the sun, or as previously stated, about 
9000 times the distance of Neptune 
from the sun, which is about 25 Vi 
trillions of miles, or 4% light years 
away. This distance is so vast that if 
we could stand on the great Alpha star 
in the Centaur and look at the sun, 
it would appear about like Polaris does 
to us here upon tne earth, and the 
most powerful telescope ever con- 
structed would not have sufficient pene- 
trating power to reach a single one of 
our planet's, not even Jupiter, as large 
as he is. 

It appears evident that there are no 
great bodies very near us and the 
solar system is in the midst of a great 
field in space, with a diameter of at 
least 50 trillions of miles across. In 
other words, it would take light 9 
years to travel from one side of this 
vast field to the other. Now a's stated 
at the head of this chapter, the sun is 
in motion, he is actually migrating, or 
on a journey. It is also known that 
he is moving at the rate of about 11 
miles per 'second. If the sun should 



38 THE MATHEMATICS 

travel at this rate immediately towards 
the nearest star, the journey would re- 
quire more than 70,000 years. So it 
appears that we are in no immediate 
danger of colliding with another great 
sun. As the 'sun is speeding through 
space at about 11 miles per second, 
attended by his planets and comets, he 
is covering nearly 350,000,000, miles an- 
nually. If Adam lived 6000 years ago, 
the sun and his family have covered 
only 2,100,000,000,000 miles since his 
day, which is only about one-twelfth 
of the distance to Alpha Centauri. 



CHAPTER NINE 

THE PLEIADES 
This beautiful and well known clus- 
ter is often called the seven stars. It 
was observed and recorded in very 
ancient times, and concerning it we find 
the following in the book of Job: 
''Which maketh Anturus, Orion, and 
Pleiades, and the Chamber's of the 
South", Job 9:9; "Canst thou bind the 
sweet influences of Pleiades, or loose 
the bands of Orion"? Job 38:31. We 
also find the following reference to it 
in the prophecy of Amos 5:8: "Seek 
him that maketh the Seven Stars and 
Orion, and turneth the shadow of 
death into morning." Homer also re- 



OF THE SKY 3 9 

fers to this group. Here we have evi- 
dence of the fact that the ancients 
studied the heavens, and were to some 
extent acquainted with the constella- 
tions and prominent objects in the 
skies. The Pleiades appear in the con- 
stellation of Taurus and are easily 
distinguished to the northwest of Orion 
and Aldebaran. They are in Right 
Ascension 3 hr. 42 m. and 23d 50m 
Northern Declination. A person with 
good eyes can see six stars, while very 
strong eyes can see three others. 

The most brilliant of the nine is 
Alcyone a third magnitude star ; Electra 
and Atlas are of the fourth; Maia, 
Merope and Taygeta are of the fifth ; 
while the three not easily seen with 
the naked eye Pleione, Calaeno and 
Asterope are of the sixth magnitude. 
As six are easily visible to the naked 
eye and formerly, the Latin poet tells 
us, seven were counted, these facts may 
be held to prove that one of them is 
variable, and has diminished in bright- 
ness, or else has disappeared. 

The moon sometimes comes between 
us and the Pleiades. It did so July 
23, 1897. The mathematics of the 
heavens is so exact that the astronomer 
can look forward and foretel the day, 
hour and minute tor a hundred or 



40 THE MATHEMATICS 

even a thousand years in advence, that 
such an event will occur. He can also 
calculate backward and tell when such 
an event actually occurred in the past. 

While the naked eye can see six or 
seven 'stars in the Pleiades, a small 
telescope brings out probably fifty; 
large telescopes with photograph-plate 
after several hours of exposure, bring 
to view fully 2326 'stars. How won- 
derful that so small a space on the face 
of the sky contains so large a number ! 

Astronomers have been laboring dili- 
gently since 1838 when the first star 
was measured, to find the distance of 
the Pleiades. The conclusion arrived 
at by Newcomb and others is, that 
Alcyone, the brightest 'star in the 
Pleiades, is 267 light years from the 
solar system. If wie could look at the 
sun at such a distance, we would be 
compelled to use a telescope, for it 
would appear as a ninth magnitude 
star, and therefore would be invisible 
to the unaided eye. Alcyone is esti- 
mated to radiate about 250 time's as 
much light as the sun. That being 
true, vast must be the dimensions of 
that great sun. 



OF THE SKY 41 

CHAPTER TEN. 
GREAT SUNS OF THE UNIVERSE. 
1. Sir his. 
This is the brightest star in the 
heavens. It is the alpha star in the 
constellation of Canis Major, or the 
Great Dog. It is found in Right 
Ascension 6 hours and 40 minutes, and 
16 degrees and 34 minute Southern 
Declination. It is approaching the 
earth at the rate of about ten miles 
per 'second. It is really overtaking the 
solar system, for the sun with his 
family of planets and moons is travel- 
ing towards that part of the heavens 
opposite to Sirius. Its distance from 
us is so vast that the light of Sirius 
requires &V2 years to come to us. This 
means that it is at least 50,000,000,000,- 
000 miles away. There are only two 
or three stars known to be nearer to 
us than Sirius. While this great sun 
i's really considered among our nearest 
neighbors, it is about twice as far 
away as Alpha Centauri, or 550,000 
times the earth's distance from the Sun. 
Stated in other words, the great Dog 
Star is 'situated in space at a distance 
18,000 times as far from the sun as 
is the planet Neptune. As Sirius is 
known to be traveling towards the 
solar system at 10 miles per second, 



42 THE MATHEMATICS 

the question haS been asked: "How 
long at this rate will it take for the 
star to overtake us ?" By a little cal- 
culation in long division it is found 
that it will require more than 158,000 
years; So there seems to be no cause 
for worrying about any immediate 
danger here. 

This great sun attracted much atten- 
tion in ancient times, so that from 
Homer on down, nearly all the poets 
referred to it. Sirius rises about ten 
o'clock in the middle of November of 
each year, and is above the horizon 
only about 10 hours. On January 1, 
it rises about half past eight P. M. 
On the 28th of January it is in the op- 
posite part of the heavens from the 
sun, and rises about the time the sun 
sets, which is about 5 o'clock. So it 
is really a beautiful winter star, and 
is still very attractive during March 
and April. Early in May it becomes 
lost in the brilliancy of the sun, and 
sets with the Sun on the 20th of that 
month. 

Considering the distance and bright- 
ness of this Star, it has been estimated 
to be at least 100 times as large as 
our Sun. It has a very interesting 
companion which was discovered by 
A. G. Clark, the great telescope maker 



OF THE SKY 43 

af Cambridge, Mass. in 1862. He dis- 
covered it with an 18-inch telescope. 
Sirius and its companion revolve 
around their common center of gravity 
in about 50 years, at a distance of 
about 1,800,000,000 miles, which is 
about the same distance of Uranus 
from the sun. 

2. Vega. 
Beautiful Vega is fourth in the order 
of brightness of all stars of the first 
magnitude, and is the most prominent 
star in the constellation called the 
Lyre. It is situated in Right Ascen- 
sion 18 hr. 34 mi., and 38 degrees 42 
minutes Northern Declination. It is 
on the opposite side of Polaris from 
Capella. The star is about 7 degrees 
farther South than Capella, but some 
20 degree's farther North than Arc- 
turus. It can be seen in the latitude of 
Minneapolis at some time during every 
night in the year; if not early in the eve- 
ning, then it can be observed during 
the morning hours of the same night. 
It is about 50 degrees from Polaris. 
The sun at Vega's distance would not 
be more than one-ninetieth as bright 
as Vega. Astronomers have estimated 
that the total light of all the 'stars 
is about equal to 750 Vegas. It is a 
bluish-white star, very beautiful, and 



44 THE MATHEMATICS 

through a telescope it has the brilliancy 
of an electric arc light, and for this 
reason it is sometimes called the "Arc- 
Light of the sky." It is a hydrogen 
star very much like Sirius, but differs 
from it in showing a small amount of 
helium. It is found near the Milky 
Way. Vega, Arcturus and Capella are 
nearly equal in brightness, but Vega 
is generally regarded as the brightest 
of the three. 

Vega is more than 21 light years 
from us, or about 2% times as far 
away as Sirius, and this means that 
it is at least 126 trillions of miles dis- 
tant. Remember that a light year is 
the distance a wave of light will travel 
in one year at the rate of 186,000 miles 
per second, and amounts to nearly 
6,000,000,000,000 miles. Vega is one of 
the very large suns of the universe 
and gives out fully 90 times as much 
light as the sun. 

The sun is moving almost in the 
direction of Vega, or to be more 
exact, it is moving towards a point in 
the sky about 5 degrees or 6 degrees 
from Vega. The relative rate of ap- 
proach of the sun and Vega is about 
10 miles per second, and at this rate 
it will take the sun 558,000 years to 
pas's by Vega. Notwithstanding we are 



OF THE SKY 45 

traveling nearly in the direction of this 
star at present, we really will never 
pass very near it. 

While Vega is now nearly 51 degree's 
from the North Celestial pole, 12,000 
years hence it will be only 4% degrees 
from the pole, and then it will be our 
pole star. 

From May on through the summer 
Vega is the most beautiful and attrac- 
tive Star in the evening sky. Early in 
May it rises as the sun is setting and 
therefore it shines all night. During 
July and August it is almost overhead 
in our latitude from 9 to 10 o'clock, 
and receives the attention and com- 
ments of star gazer's generally. In 
the month of November it sets some- 
where about 1 o'clock at night, and in 
January about 9 P. M. 

Herschel proved mathematically that 
if Vega should be removed 10 times 
its present distance from the sun (at 
which time it w r ould be more than 
210 light years distant), it would be a 
star of the sixth magnitude, and would 
then only be just visible to the un- 
aided eye. If it should be removed 
100 times its present distance, it could 
still be seen with moderate telescopes. 
If it should plunge into space 1,000 
times its present distance or 21,000 



46 THE MATHEMATICS 

light years, it would still be visible in 
the largest telescopes. 

3. Aide bar an. 
This is one of the six very brilliant 
winter stars, and the other five are: 
Betelgeuse, Rigel, Pollux, Procyon, and 
Sirius. It is found in Right Ascen- 
sion 4 hr. 31 m. and 16 degree's 20 
minutes Northern Declination. It is 
indeed a great red sun, or star of the 
first magnitude, in the eye of Taurus, 
the Bull. It i's the most brilliant star 
in the Hyades, which group is situated 
about 9 degrees Southeast of the Pleiades. 
This star i's about 15 degrees North- 
west from Betelgeuse, and about 35 
degrees Northwest trom Sirius. Con- 
sidering these facts, and being a 
magnificant red star, it is not difficult 
to locate on the face of the sky. Of 
the first magnitude stars, Aldebaran is 
fourteenth in order of brilliancy. It 
ha's been estimated that the sun gives 
us 90,000,000,000 times as much light 
as this star, but if it were brought as 
close to us as the sun, it would give 
us 45 times as much light as we re- 
ceive from the sun. It must therefore 
be many times larger than our Sun. 
So vast is its distance from us that it 
requires 28 year's for its light to reach 
the human eye, and this means that it 



OF THE SKY 4 7 

is nearly 168 trillions of miles away. 
The spectro'scope shows that this star 
is speeding through space and away 
from the sun at the rate of 30 miles 
per second; but it must travel on at 
this rate for more than a thousand 
years before it will add another trillion 
of miles to its distance. Aldebaran 
rises about an hour after the Pleiades 
at which time it is almost directly 
under this group. It shows its bright 
red face in the evening sky for fully 
8 months in the year. In the early 
days of October it rises between 9 
and 10 o'clock P. M., and shines the 
remainder of the night. In the early 
part of December it rises about the 
time the 'sun is setting, and requires 
about 7 hours to reach the meridian. 
During the last days of May it be- 
comes lost in the brilliancy of the 
sun, and during the month otf July it 
rises and can be observed a short time 
before sunrise. 

The moon many times in its passage 
through the heavens comes between 
us and Aldebaran, at which times of 
course the star is hid from our view. 
Astronomers can calculate ahead of 
time a year, or a thousand years as 
to that matter, just when a happening 
of this kind will occur. This is an- 



48 THE MATHEMATICS 

other evidence of the exactness of 
astronomical mathematics. 



CHAPTER ELEVEN. 
OTHER GREAT SUNS. 

4. Capella. 

Capella is a magnificent star of the 
first magnitude in Auriga, the Chario- 
teer. It is about 40 degrees from the 
Big Dipper, situtated a little more than 
half way from Polaris to Bellatrix, 
and is closer to Polaris than any other 
of the very bright stars. Its Right 
Acension is the same as that of Rigel 
in Orion, being 5 hr. 10 m., and 45 
degrees 54 minutes Northern Declina- 
tion. Capella is a yellow star with 
golden rays, like our sun, and the 
'spectroscope reveals the fact that there 
is vapor of iron, sodium and many 
other metals in its composition. It is a 
spectroscopic binary. While Capella is 
one of the comparatively near stars to 
the solar system, it it really a little 
more than 34 light years distant, or 
over 200 trillions of miles away. This 
means that it is 4 times the distance 
of Sirius, and 72,000 times Neptune's 
distance from the sun. The sun at 
its distance would be at about the 



OF THE SKY 49 

limits of visibility without the use of 
a telescope. 

Should Capella be brought as near 
to us as the sun, it would be 60 times 
as bright as he is. It is really re- 
ceding from us at the rate of about 
15 miles per second, 900 miles per 
minute, 54,000 mile's per hour, or more 
than a million miles per day. It has 
been calculated to radiate more than 
200 times as much light as the sun, 
but it is believed to have lost some of 
its luminosity within the past few 
years. This star being 'situated more 
than half the distance from the celes- 
tial equator to the North Pole is above 
the horizon fully 20 hours out of every 
24. In other words, from the time it 
sets till it rises again is only about 
4 hours, and for this reason it can be 
seen at some time during the night of 
every month in the year. Early in 
August it rists about 10 o'clock at 
night and shines the remainder of the 
night. During July it is too close to 
the sun to be viewed with satisfaction, 
but in the month of October it rise's 
about the time the sun is setting and 
therefore shines all night. While Capella 
appears to the naked eye to be a single 
star, it is really a great spectroscopic 
binary system, and its companion lies so 



SO THE MATHEMATICS 

near to it that they revolve around their 
common center of gravity in about 104 
days. 

5. Arcturus. 

"Canst thou guide Arcturus with his 
sons ?" Job. 38 : 32. "Which maketh 
Arcturus, Orion and Pleiades, and the 
Chambers of the South." Job. 9 : 9. 
Job must have been something of an 
astronomer, although he lived in the 
earliest days of authentic history. This 
is a magnificent star of the nYst magni- 
tude in the constellation of Bootes, 
the Bear Driver, and is situated in 
the left knee. It is found in Right 
Ascention 14 hr. 12 m., and 19 degrees 
39 minute's Northern Declination. With 
Denebola and Spica it iforms a large 
equilateral triangle. It is not difficult 
to locate in the heavens for the handle 
of the Big Dipper when prolonged with 
a continuation of the curve which it 
possessed leads to Arcturus. No other 
very bright star is near it. 

It is one of the great sun's of the 
universe, and is often called a "run- 
away star," because it is known to be 
speeding through space at a prodigious 
rate, probably not less than 200 miles 
per second, or more than 17,000,000 
miles per day. But its distance from 



OF THE SKY 5l 

us is so vast that a century would be 
required for it to pass over a space on 
the face of the sky equal to one-eighth 
the diameter of the moon. 

It outshines any other 'star in the 
Northern heavens unless it be Capella. 
There is a rivalry between Capella, 
Arcturus and Vega as to brightness, 
but those who have given most atten- 
tion to the subject have concluded that 
Capella is the most luminous of the 
three. Arcturu's is at least 12 times as 
far away as Sirius, and still more 
vast in its dimensions, for its bulk is 
believed to be at least 3,000 times that 
of the latter star. Its great luminosity 
and the vastness of its distance are 
proofs of its ponderous size. Its 
spectrum closely resembles that of the 
sun, and not les k s than 100 years are 
required for its light to come to us. 
Its light-giving power is equal to that 
of perhaps 1,300 'suns such as ours. 

Arcturus is about 20 degrees south- 
west of the constellation, Corona Bo- 
realis. In the early nights of March 
it rises about 8 o'clock, while on April 
first it comes up about the time the sun 
is setting and of coufse shines all 
night. In order that you may keep 
along well with its position in the sky 
and know where it is, you will find 



52 THE MATHEMATICS 

it almost overhead early in the night 
June 15 and it 'slowly floats towards 
the northwest during July. 

If our sun were as distant as is 
Arcturus, it would really be a tele- 
scopic object because it could be seen 
only through a telescope, entirely in- 
visible to the unaided eye. 



CHAPTER TWELVE. 
CANOPUS THE GREAT SOUTH- 
ERN STAR. 

Of the five very beautiful first mag- 
nitude stars too far south for ob- 
servation in our latitude, the name's 
of which being Alpha Centuari, Beta 
Centauri, Alpha Crucis, Achernar, and 
Canopus, the latter can be seen in 
southern Florida and Texas for a short 
time only as it does not remain above 
the horizon long at a time. All of 
them are visible from the West In- 
dies southward. 

Canopus is known as the great star 
of prehistoric Egypt, and brightest of 
the entire heavens except Sirius. It is 
situated in Right Ascension 6 hr. 22 m., 
and 52 degrees 39 minute's Southern 
Declination. It is therefore less than 
38 degrees from the South Celestial 
pole. It yields no appreciable parallax 
as it has no appreciable proper motion. 



OF THE SKY 53 

It seems to be situated among stars 
of the eight magnitude if not farther. 
It must for this reason have at least 
10,000 times the light-giving power of 
the sun. At this distance the sun 
would long have ceased to be visible 
to the. naked eye. As Canopus is a 
solar type of a star, its density and 
temperature must be somwhere near 
the sun's. If the luminosity of Cano- 
pus is 10,000 times that of the sun, 
it follows that its diameter is at least 
100 times the sun's, because the sur- 
faces of globes are to each other as 
the squares of their diameters. Cano- 
pus is without doubt one of the greatest 
bodies in the universe known to astro- 
nomers, and believed from the above 
reasons and from many other facts to 
be at least 1,000,000 times larger than 
the sun. The volumes of globes are to 
each other as the cubes of their dia- 
meters. If the diameter of Canopus is 
100 times that of the sun, then its 
volumt is 1,000,000 times that of the 
sun. We learned in Chapter Two that 
the volume of the sun is 1,300,000 times 
that of the earth. That being true, 
the volume of Canopus is 1,300.000,000,- 
000 times that of the earth. 

Great as Arcturus is, it is probable 
that Canopus is at least 300 times 



54 THE MATHEMATICS 

greater. While Canopus yields practi- 
cally no parallax and its distance has 
not therefore been measured by that 
means, yet for various other reasons 
it seems evident that it is at the lea'st 
estimate 310 light years from the solar 
system. This means that this great 
southern sun is 1,860 trillions of miles 
away, or expressed in other figure's it 
is about 20,000,000 times further from 
the earth than is the sun. 



CHAPTER THIRTEEN. 

REGULUS THE GREAT ECLIPTIC 

SUN. 

This i's called Cor Leonis, the Lion's 
Heart, and by astronomers Alpha 
Leonis. It is located in the Constel- 
lation, Leo, in Right Ascension 10 hr, 
4 m. and 12 degrees 24 minutes North- 
ern Declination. It is very nearly on 
the ecliptic being almost covered by 
the sun on the 20th of August a l s each 
year rolls around. It is many times 
hidden from our view by the moon, 
because that body in its revolutions 
around the earth comes between us 
and that sun. 

Regulus is about 60 degree's a little 
North of West from Arcturus, and is 
easily recognized as the brightest star in 



OF THE SKY 5 5 

the Constellation. This star is of 
unusual interest because of the fact 
that the November Meteors, or the 
Leonids, seem to approach the earth 
from a point a few degrees North of 
it. While it i's doubtless many times 
larger than Sirius, it has anly 1/13 of 
the brightness of that star, because of 
its vast distance from us. 

Regulus is really a great telescopic 
triple, i. e. while the naked eye can 
see only one star, the telescope re- 
solves it into 3 great suns. The posi- 
tion of Regulus was found by Baby- 
lonian astronomers upwards of 4,000 
years ago. It was at that time in 
longitude 119 degrees, while it is now 
more than 148 degrees. 

During the months of June and July 
Regulus can easily be found about 50 
degrees a little North of West from 
the bright "star, Spica, in the constella- 
tion Virgo, and at that time it will 
be low in the West. It can be ob- 
served in both winter and summer, and 
is really visible the first half of the 
night for about 2 /z of the year. It 
rise's at 9 P. M. during the last half 
of December, and continues to be the 
most conspicuous star in the eastern 
'skies till the appearance of Vega and 
Arcturus a little later. Between 6 and 



56 THE MATHEMATICS 

7 hours after it rises it reaches the 
meridian, at which time it i's about 
60 degrees above the horizon, and 
about 30 degree's from the zenith. 
During the first 3 months of the year 
it shines all night, and in the month 
of February it rises about the time 
the sun i"s setting. During the fall 
months of October and November, it 
shines beautifully in early morning 
hours. 

Regulu's is certainly one of the very 
great suns of the universe in dimen- 
sions, and is estimated to send out 
1,000 times as much light a's the sun. 
It must therefore be many thousands 
of times larger. Its distance from the 
earth is so vast that it requires 162 
years for its light to come to us. 



CHAPTER FOURTEEN. 
POLARIS AND ITS MANY 

LESSONS. 
Polaris, the brightest star in the 
constellation, Ursa Minor, The Little 
Bear, is located in Right Ascension 1 
hr. 27 m. and 88 degrees 50 minutes 
Northern Declination. Polaris, Deneb 
and Vega form a right-angled triangle 
of which Deneb is in the right angle. 
This triangle is not difficult to find, 
and it ifc a splendid way to find the 



OF THE SKY 5 7 

North Star. A line drawn from the 
bright red star, Antares, about midway 
between Arcturus and Vega and con- 
tinued till the entire length is 116 
degrees will reach Polaris. Another 
way to find Polaris is to imagine a 
line drawn through the "pointers" of 
the Great Dipper and extended about 
25 degrees from the nearest pointer to 
Polaris. 

This star is the center of the North- 
ern Stellar company of stars, and 
several beautiful constellations revolve 
around it every 24 hours, among them 
being Cassiopeia and the Big Dipper. 
This star is also the center of a 
circling system of its own. It travels 
around the North Celestial Pole in a 
very small circle of less than 2% de- 
grees in diameter. In this circle are 
many invisible stars. More than 75 
have been seen through telescopes, 
and fully 200 have been counted on 
photographic plates. There is a 9th 
magnitude star, therefore telescopic, 
almost exactly at the pole. Polaris is 
a double star, its companion is of 
about the 9th magnitude, and the 
spectroscope has revealed the fact that 
there are two almost dark companions 
revolving around Polaris. In reality it 
is a telescopic double, and the brighter 



58 THE MATHEMATICS 

component of the double star is really 
a spectroscopic triple. So when we 
look at Polaris we really look at 4 
star's, though apparently only one. 

Remember that Polaris is estimated 
to be 44 light years from the solar 
sy'stem, and is really one of our nearest 
neighbors. Notwithstanding, if an 
aeroplane should start today to Polaris, 
traveling continuously night and day 
at 200 mile's per hour, or 4,800 miles 
per day, it would require more than 
150,000,000 years to make the journey. 
Let us use another illustration. Sup- 
pose we were connected with Polaris 
by telephone, and a message should be 
started today over the wire. It would 
be 44 years before it would be heard 
on Polaris, and another 44 years would 
be required to get a reply. We are 
supposing here that a me'ssage by 
electricity travels at the same rate of 
speed as light, viz., 186,000 miles per 
'second. 

On account of the precession of the 
equinoxes Polaris will not always be 
our pole star. The North Celestial 
pole is slowly approaching Polaris and 
in 2095 it will be within less than one- 
half degree from the star, at which 
time it will begin to recede, and in 
about 12,000 years Vega will be our 



OF THE SKY 59 

pole star. Then the pole will begin to 
recede from Vega and will continue 
to do so till after the lapse of another 
12,000 year's, when Polaris will again 
be our pole star. 



CHAPTER FIFTEEN. 

DENEB THE GREAT SUN IN 
CYGNUS. 

The word Deneb comes from the 
Arabic. The catalogue name is Alpha 
Cygni, The Swan. It is a very beauti- 
ful white star, and is located in Right 
Ascension 20 hr. 38 m., and 44 degrees 
57 minutes Northern Declination. It 
is in one of the finest of the constella- 
tions. This constellation may be easily 
recognized by the shape of a cross 
formed by its 5 principal stars, Deneb 
being the brightest and the most 
Northern. This constellation is noted 
because the first star whose ditance 
to be measured is located in it. Its 
catalogue name is 61 Cygni. Its paral- 
lax was found and the star's distance 
was measured in 1838. It was found 
to be about 8 light years distant as 
stated in Chapter Six. 

Deneb yields no appreciable paral- 
lax which is proof that the star is of 
vast distance from us. Its luminosity is 
so great that it must be many times 



60 THE MATHEMATICS 

larger than the sun. When a star 
yield's a parallax, its distance can be 
measured by that method. Otherwise 
its distance must be calculated in some 
other way. Upwards of 60 stars have 
yielded a parallax and their distances 
measured. 

This star appears above the horizon 
about 19% hours from the time it 
rises till it 'sets. The great Northern 
Cross of which Deneb is a part covers 
about 20 degrees in the Milky Way. 

Of the 20 first magnitude stars, 
Deneb is the lowest in apparent bright- 
ness, but it is likely among the largest 
in actual 'size. Its light-giving power 
must, therefore, be vast. Astronomers 
have announced that the star is ap- 
proximately 325 light years from the 
solar system, or 1,950,000,000,000,000 
miles. A canon ball traveling at the 
rate of 1,750 ft. per second would re- 
quire nearly 185,000,000 years to span 
the distance. 

Deneb is coming towards us at the 
rate of 30 miles per second, and if it 
continues to come at that rate, it will 
be 2,063,000 years before it arrive's. 
As this star is above the horizon nearly 
5/6 of the time, it can be observed 
Sometime between sunset and mid- 
night during every night in the year. 



OF THE SKY 61 

While it shines with less brightness 
than the other first magnitude stars, it 
is very beautiful during January and 
February. It rises about the time 
the sun is setting in May, and shines 
all night. At the opposite end of the 
cross from Deneb is Albireo, which 
the telescope resolves into two stars. 
The components are about 35 seconds 
of a degree apart, appearing to the 
naked eye as only one star, but a small 
telescope easily shows the two. 



CHAPTER SIXTEEN. 

RIGEL THE GREAT ELECTRIC 
SUN OF ORION. 

This beautiful Southern star is situat- 
ed in one of the finest constellations 
in the southern sky, if not in the en- 
tire her^ens. It shows itself splendid- 
ly all through the winter months in 
the evening sky. 

It is located in Right Ascension 5 hr. 
10 m., and 8 degrees 18 minutes South- 
ern Declination. It is a little more 
than 50 degrees exactly south of Ca- 
pella, and about 20 degrees southwest 
of Betelgeuse. The Belt of Orion is 
situated nearly on the equator and 
about midway between Rigel and Betel- 
geuse. 

Rigel is a first magnitude star and 



62 THE MATHEMATICS 

haS been found to be a telescopic 
double, both components being bluish- 
white in color. They are about 10 
seconds of a degree apart. It is with- 
out doubt one of the great suns of 
the universe in point of size and light- 
giving power. From the proper mo- 
tion of this star it is estimated to be 
at least 330 light years distant and 
this being true, its light-giving power 
must be at least 8,000 times that of 
the sun. As light travels nearly 6,000,- 
000,000,000 of mile's per year, in 330 
years it would travel 1,980 trillions of 
miles, and this represents the distance 
to Rigel in miles. This distance is 
so vast, that the figures by which it 
is expressed, daze the mind. There- 
fore, when you are looking at Rigel 
you are beholding a star 700,000 times 
Neptune's distance from the sun; near- 
ly 78 times the distance to the nearest 
fixed star; more than 11 time's Vega's 
distance from the sun; and 7% times 
the distance of Polaris from our own 
great luminary. 

The 'spectroscope reveals the fact 
that Rigel is needing from the solar 
system at the rate of 15 miles per 
second. If it continued to travel 
from us at this rate, to cover a dis- 
tance representing only 1 per cent of 



OF THE SKY 63 

the present distance, it must spend 41,- 
800 years. 



CHAPTER SEVENTEEN. 

THE SOLAR SYSTEM BOUND TO- 
GETHER BY LAW. 

The solar system is composed of the 
sun, 8 planets, nearly 600 asteroids, 26 
moons, and a number of comets that 
go out into space and return periodical- 
ly. Not a single member of the system 
is at rest. All are in motion, and 
certain laws govern these motions. 
The operation of a few beautiful laws, 
mathematically expressed, keep all these 
hundreds of bodies in motion and yet 
hold them in place, so that unity reigns 
and order and beauty are seen and 
observed in every part. The mathema- 
tics of the whole system is so well 
in hand, that the astronomer knows 
simply by looking at his chart where 
any of the members of the system are 
at any given time during the year. 

We owe much if not all to such 
men as Kepler, Newton, Tycho Brahe, 
Galileo, etc., for our knowledge con- 
cerning these laws, and the perfect 
working of the system. 

Let us keep in mind Newton's Uni- 
versal Laiv of Gravitation : "Every 



64 THE MATHEMATICS 

particle of matter in the universe at- 
tracts every other particle of matter 
with a force directly proportional to 
the product of their masses, and de- 
creasing as the square of the distance 
between them increases." 

It is by this law that the sun holds 
all his planets and periodic comets 
in place, and the planets hold all their 
respective satellites or moons in pro- 
per position. Some comets, for exam- 
ple, go out into space enormous dis- 
tances from the sun, traveling for hun- 
dreds or even thousands of years, but 
by the universal law of gravitation 
they are compelled to return. As an 
illustration, Comet II of 1844 will 
travel away from the sun for 51,025 
years reaching its aphelion distance at 
a point in space 143 times the distance 
otf Neptune, or 4,366 times the earth's 
distance from the sun, in round num- 
bers 400 billions of miles. But on ac- 
count of the Superiority of the sun 
(for he is 750 times greater than all 
his planets, asteroids and moons com- 
bined), this comet will be compelled 
to return, and it will require another 
51,025 years for it to return in peri- 
helion. 

Let uS also remember Newton's First 
Law of Motion: "A body once in mo- 



OF THE SKY 65 

tion would move iorever in a straight 
line, if it were not acted on by some 
external force." By keeping these 
two laws in mind, we are able to un- 
derstand why the planets and asteroids 
are not allowed by the sun to fly off 
into space, but are compelled to revolve 
around him at regular distances and 
definite times which are well known. 
These bodies already in motion would 
move in a straight line, according to 
the first law of motion, if it were not 
for the overruling power of the sun 
compelling them to travel in curved 
paths. 

The 'sun is the great center of the 
system, 750 times greater than all the 
planets combined. They travel around 
the sun in almost perfect circles. The 
law is, the nearer a planet is to the 
sun, the faster it must travel to keep 
from being drawn to him. The law 
of universal gravitation explains the 
reason why that Mercury, the nearest 
planet to the sun travels at the rate 
of 30 miles per second, while Neptune, 
the outermost planet, travels at the 
rate of only 3% miles per second. If 
Mercury's rate were only 3% miles per 
second, it would be slowly but surely 
pulled to the sun. If Neptune^ rate 



66 THE MATHEMATICS 

were 30 miles per second, it would fly 
off into the infinite depths of Space. 
The sun's pulling power at Neptune's 
distance is not near so great as it is 
at Mercury's distance, for by the law 
of universal gravitation aS stated above, 
the attractive power of the sun "de- 
creases as the Square of the distance 
increSaes." 

We find that there is a regular de- 
crease in the rate of motion of all the 
planets from Mercury to Neptune, as 
follow's : 

1. Mercury is 36,000,000 miles from 
the sun, completes a revolution around 
that body in 88 days, and travel's at 
the rate of 30 mile's per second. 

2. Venus is 67,000,000 miles from 
the sun, completes a revolution around 
him in nearly 225 days, and travels at 
the rate of 22 mile's per second. 

3. The earth is 93,000,000 miles from 
the sun, completes a revolution in 365 
day's, and travels at the rate of ISY2 
mile per second. 

4. Mars is 141,000,000 miles from 
the Sun, completes a revolution in 687 
days, and travels at 15 miles per sec- 
ond. 

5. Jupiter is 483,000,000 miles dis- 
tant from the sun, completes a revolu- 
tion in nearly 12 years, and travels at 
about 8.1 miles per second. 



OF THE SKY 67 

6. Saturn is 886,000,000 miles from 
the Sun, completer a revolution in 
about 29Mj years, and travels at 6 
miles per second. 

7. Uranus is 1,800,000,000 miles dis- 
tant from the sun, completes a revolu- 
tion in 84 years, and travels at 4.2 
miles per second. 

8. Neptune is 2,800,000,000 miles 
from the sun, completes a revolution 
in not quite 165 years, and travels at 
the rate of 3% mile's per second. 

The same laws hold good relative 
to the various planets in relation to 
their respective moons. There are 
known to be 26 moons in the Solar 
system. The earth has 1 ; Mars has 2 ; 
Jupiter has 8; Saturn has 10; Uranus 
has 4; and Neptune has 1. 

Our own moon is 238,840 miles from 
the earth, completes a revolution in 
27 d. 7 hr. 43 m. lis., and travels 
at the rate of about ^ of a mile per 
second. 

Mars' inner moon, (Phobos) is so 
near the planet, (5,850 miles) that is 
completes a revolution in 7 hr. 39 m. 
15"s, and travels at the rate of 1% 
miles per second. In other words it 
travels around Mars 3 times in about 
one of our days. While his outer 
moon, (Deimos) being about 2Y2 times 



68 THE MATHEMATICS 

as far away, (14,650 mile's), completes 
a revolution in 1 d. 6 hr. 17 m. 54 s., 
and travels at the rate of only .9 of a 
mile per second. 

Jupiter's nearest moon i^ 112,000 
mile's from the planet, completes a 
revolution in a little less than 12 hours, 
and travels at the ra*e of 14 miles per 
second; while his outermost moon is 
7,403,000 miles distant (nearly 66 times 
as far from the planet as his innermost 
moon), completes a revolution in 265 
days, and travels at the more moderate 
rate of a little more than 2 miles per 
second. 

Saturn's innermost moon, (Mimas) 
is 117,000 miles from the planet, com- 
pletes a revolution in 22 hr. 37 m. 5s., 
and travels at the rate of nearly 9 
miles per second; while his outermost 
moon, (Phoebe) is 8,000,000 miles dis- 
tant (more than 68 times as far from 
the planet a's his innermost moon), 
completes a revolution in 546 days, and 
travels at the rate of a little more 
than 1 mile per second. 

Uranus' nearest moon, (Ariel) is 
120,000 mile's distant, completes a re- 
volution in a little moore than 2% 
days, and travels at 2% miles per sec- 
ond; while his outermost moon, 
(Oberon) is 365,000 milefc away, com- 



OF THE SKY 69 

pletes a revolution in 13 d. 11 hr. 7 m. 
6s, and travels at nearly 2 miles per 
second. 

Neptune's moon is 221,500 miles dis- 
tant, completes a revolution in 5 d. 21 
h. 2 m. 44 s., and travels at the rate 
of 27 miles per second. 

We must also keep in mind Kepler's 
Third Law: 'The squares of the times 
of revolution oif the planets about the 
sun are proportional to the cubes of 
their mean distances from the sun." 

This is a beautiful law, and is a con- 
vincing argument that nature is built 
on law and order. It is also positive 
proof that design and intelligence are 
back of all things and the cause of 
all things. 

Under the word Time below will be 
found the number of years or fraction 
of a year that the planets require to 
revolve around the sun. Under the 
words Mean Distance will be found 
the figures representing the number of 
millions of miles that the planets are 
situated from the Sun. 

Tune Mean Distance 
The earth .. 1.00 year 93 mil. miles 

Mercury 24 36 

Venus 62 67 

Mars 1.88 141 

Jupiter 11.86 141 



70 THE MATHEMATICS 

Saturn 29.46 886 

Uranus 84.00 1800 

Neptune ....164.78 2800 

Applying the above law, we can 
tform a number of proportions, 'showing 
the beautiful mathematical relations of 
the planets to each other. The figures 
especially under Mean Distance are on- 
ly approximate, not intended to be 
scientifically exact, but simply stated 
in round numbers. 

We can u'se any pair of planets in 
forming the proportions. To illustrate: 

The earth's time (1 year) 2 is to 
Mercury's time (.24 year) 2, as the 
earth's mean distance (93 million) 3 is 
to Mecury's mean distance (36 mil- 
lions) 3. 

Performing the operation, you will 
find that the product of the means will 
equal the product ot the extrems, i. •. 
it will be approximately so. 

In the same way you can use any 
two of the planets above with like 
results, by applying Kepler's Third 
Law. 

Let us consider another example: 

Suppose we know the earth's 
time and mean distance; we also know 
Uranus' time, but we do not know 
Uranus' mean distance. How can we 
find the mean distance? As follows: 



OF THE SKY 71 

1 squared is to 84 squared as 93 
cubed is to x cubed. 

We let x represent the unknown 
mean distance here. The product oi 
the extremes being equal to the product 
of the mean's, x will be found to 
equal the cube root of 84 squared mul- 
tiplied by the cube of 93. The result 
will be approximately 1800, which 
means 1800 millions of miles, approxi- 
mately the distance from the sun to 
Uranus. 



CHAPTER EIGHTEEN 

ALGOL THE GREAT VARIABLE 

SUN IN PERSEUS. 

This famous Variable Star belongs 
to the Sirian type as its spectrum in- 
dicates. It seems to have been red 
hundreds of years ago, but now it is 
white, or slightly yellowish. 

It is located in Right Ascension 3 h. 
2 m., and 40 degree's and 34 minutes 
Northern Declination. It is a fixed 
star in Medusa's Head, in the constel- 
lation, Perseus, its catalogue name be- 
ing Beta Persei. It is remarkable for 
its variation in brightness. The name 
Algol is Persian in origin, and means 
the "demon," which indicates that the 
ancients most likely observed some 
peculiarities in its behavior. 



72 THE MATHEMATICS 

The periodical changes in its bright- 
ness seem to be the result of eclipses 
by ^ dark satellite, which comes be- 
tween us and the star. The variability 
of Algol was discovered in 1667, by 
Montanari, but the English astronomer, 
Goodricke, wa*s first to give a satis- 
factory explanation of its variability in 
1782, now 138 years ago (this 1920). 

In 1889, Vogel fully demonstrated 
by use of the spectroscope, that Algol 
is really a binary system, and is called 
a spectroscopic binary, with a dark 
companion revolving around it, whose 
plane passes nearly through the solar 
system. 

Algol is usually a star of the second 
magnitude, but at regular intervals of 
2d 20h 48m 54s it falls to nearly the 
fourth magnitude; it remains faint (for 
only about 20 minutes, and then re- 
kindles until it reaches its usual bright- 
ness. The variation of its light con- 
tinues during 9 hrs. and 45 m. of each 
period. 

Both components are in motion and 
both revolve around their common cen- 
ter of gravity of the pair. Vogel 
found by studying this star with the 
spectroscope, that a little before a 
minimum of light takes place, the dark 
Companion is approaching us, and the 



OF THE SKY 73 

bright companion is receding. After 
the minimum of lignt is over, the mo- 
tion of the two bodies is reversed, the 
bright one approaching us, and the 
dark companion receding. This is 
exactly as it should be in a system of 
this kind. The components seem to be 
about 3,230,000 miles apart, the dia- 
meter of Algol being estimated to be 
1,000,000 miles, and that of its dark 
companion, 800,000 miles, nearly as 
large as the sun. Algol, the brighter 
of the two, is estimated to be at least 
fifteen times as bright as the sun. 

While this star yields no parallax, it 
has been estimated to be not less than 
23 light years from the sun, and this 
great system is approaching us. 

Remember that this periodic variation 
in the brightness of Algol is regular, 
and astronomers can calculate for a 
hundred years ahead of time exactly 
when an eclip l se will begin and end, as 
easily as they can an eclipse of the 
sun or moon. This is but another 
argument in favor of the exactness of 
astronomical mathematics. 



74 THE MATHEMATICS 

CHAPTER NINETEEN* 
CASTOR AID POLLUX 

"And after three months we departed 
in a ship of Alexandria, which had 
wintered in the isle, whose sign was 
Castor and Pollux." Acts. 28:11. 

Anciently favorable navigation was 
believed to have been brought about 
by the influence of the'se stars, and the 
ship in which Paul sailed away from 
Melita bearing the sign of Castor and 
Pollux carried him safely on towards 
Rome. 

These are the two brighest stars in 
the constellation Gemini. Pollux whose 
catalogue name is Beta Geminorum is at 
present the brighter of the two, and is 
the only fiYst magnitude star to be 
found in the constellation. But three 
centuries ago this order of luminosity 
was reversed, and Castor outshone Pol- 
lux. These brothers are distant only 
about 4 or 5 degrees. Castor rises 
something like 20 to 25 minutes earlier 
than Pollux, both appearing at nearly 
the same time in which Rigel and 
Betelgeuse rise. 

Gemini in which Castor and Pollux 
are located is one of the zodiacal con- 
stellations, and is on the opposite 'side 
of the Milky Way irom Taurus and 



OF THE SKY 7 5 

Orion. The sun enters Gemini May 
20th of each year. 

Pollux is situated in RightAscension 
7 h 40 m and 28 degrees 15 minutes 
Northern Declination. Castor, or 
Alpha Geminorum is situated in Right 
Ascension 7 h 29 m, and 32 degrees 5 
minutes Northern Declination. These 
two stars are about 25 degrees North 
of Procyon, the only first magnitude 
star in the constellation Canis Minor, 
the Little Dog. It is probable that 
Pollux will continue to gain in lumin- 
osity over Castor, for the 'spectroscope 
shows that Castor is going away from 
the solar system at nearly 5 miles per 
second, while Pollux is approaching at 
about 33 miles per second. Pollux is 
estimated to be at least 54 light years 
from the solar system, or more than 
324 trillion miles. If the star continues 
to approach the earth at above rate, 
it will take more than 311,000 years to 
reach us. 

Castor has been found to be a great 
binary system, and the two components 
can be easily separated by a 'small tele- 
scope. The two stars, Castor and his 
component, are revolving slowly around 
their common center of gravity, and 
while it has been about two centuries 
since they were found to be double, 



76 THE MATHEMATICS 

they have really completed only about 
one-fifth of a revolution, the period be- 
ing nearly 1000 years. The spectro- 
scope has revealed the fact that the 
fainter component is also a double 
fetar, one of them being opaque. It 
takes only about 3 days for these two 
ta make a revolution. Thus Castor is 
known to be a system of 3 stars, 
though apparently only one. 

There are many other wonderful les- 
sons to learn about Gemini. If you 
examine with the unaided eye a small 
part of Gemini which contains Castor 
and Pollux, and then look through a 
six-inch reflector letting it cover the 
'same space, you will be greatly sur- 
prised to find that while only 10 stars 
are visible to the naked eye more than 
3200 can be seen distinctly through 
the telescope, some of them being stars 
of the 13th magnitude. If you should 
examine this same field looking through 
one of the most powerful telescopes of 
the present day, you would doubtless 
find many thousands more of stars, 
some of them being of the 14th, the 
15th, the 16th and the 17th magnitudes. 



OF THE SKY 11 

CHAPTER TWENTY 

PROCYONi THE GREAT WHITE 

STAR IN THE LITTLE DOG 

This very beautiful white star is in 
Right Ascention 7 h 35 m, and 5 de- 
grees and 27 minutes Northern Declina- 
tion. It is the only bright star in the 
constellation Canis Minor, or the 
Lesser Dog. The light-giving power 
is fully 8 times as great as the sun, 
and its velocity at right angles to the 
line of sight is about 12 miles per 
second. Its spectrum is said to be inter- 
mediate between that of Sirius and the 
sun. This star is one of our near 
neighbors, but it is fully 10 light years 
away, or about 60,000,000,000,000 of 
miles. If a canon ball should be 
started there today, traveling at 20 
miles per minute, or nearly 29,000 
miles per day, it would require 5,707,000 
years to span the distance. 

Procyon is about 23 degrees almost 
exactly south of Pollux, and with 
Betelgeuse and Sirius it forms an 
equilateral triangle. It rises a few 
minutes earlier than Sirius. The 'spec- 
troscope reveals the fact that this great 
star is approaching the sun at 6 miles 
per second, and if it continues to come 
towards us at this rate, it will take 



78 THE MATHEMATICS 

more than 317,000 years to complete 
the journey. 

Procyon is found to be a great 
'binary system with a companion of 
the 13th magnitude, the distance be- 
tween the two components being 5 sec- 
onds of a degree. While the com- 
panion star is faint, it is relatively 
(very massive, and rts presence first 
became known by the large irregular- 
ities which its attraction produces in 
the motion of the principal star Procyon. 
The great Lick telescope situated on 
Mount Hamiltos, Calif., discovered the 
disturbing companion in 1895. The 
period of revolution of this great 
binary system about their common cen- 
ter of gravity is 40 years, in an orbit 
of about 1,800,000,000 miles. In other 
words, these two great suns are about 
as far from each other as Uranus is 
from the 'sun. 



CHAPTER TWENTY-ONE 

THE SEVEN GREAT SUNS OF 
THE BIG DIPPER 

The beautiful and very conspicuous 
constellation Ursa Major, or the Great 
Bear, contains 133 stars that can be 
seen with the unaided eye. It is one of 
the great circum-polar constellations, 



OF THE SKY 79 

revolves around the North Pole of the 
heavens every twenty-four hours, and 
never goes below the horizon in the 
latitude of the United States. This 
con'stellation contains 7 stars, 6 of the 
second magnitude and 1 of the fourth 
magnitude, which form the Big Dipper, 
or Charles's Wain as it is called by 
English astronomers. The stars Alpha 
and Beta, or Dubhe and Merak, are 
called the Pointers, because a line 
drawn through these two stars and 
extended northward about 5 times the 
distance they are apart will terminate 
near Polaris, our present pole star. 
So after locating the Big Dipper it is 
an easy matter to find the pole star. 
The other five stars forming the dip- 
per are, Phecda, Megrez, Alioth, Mizar 
and Benetnasch. Those astronomers 
who have given much attention to 
the study of the proper motion of 
stars have found that 5 stars of the 
dipper are traveling away from the 
sun at about 17 miles per "second, 
while the other two are drifting in 
the opposite direction. From these 
circumstances it is evident that the 
dipper will not always hold its present 
form, but will in future ages be pulled 
apart. 



80 THE MATHEMATICS 

Mizar at the bend of the handle is 
a very beautiful double star, requiring 
only a small telescope to get a good 
view of it. It was really the first dou- 
ble system to be discovered and was 
in the year 1650, only about 40 years 
after Galileo invented and used the first 
real telescope. These two great stars 
complete a revolution around their 
common center of gravity in about 20,- 
000 years. The spectroscope reveals 
the fact that there is a third 'star re- 
volving about Mizar in something like 
104 days, this latter star being nearer 
Mizar than the other one. So when 
you look at Mizar, you really look at 
3 great suns, thougn apparently only 
one. This great system is calculated to 
be fully 40 times as great in mass as 
our sun. A keen eye can see the faint 
'star Alcor not far distant from 'Mizar. 

By far the brightest of these great 
suns is Alioth, the star between the 
bend in the handle and the junction 
of the handle with the bowl of the 
dipper. It comes near being a first- 
magnitude star in brightness. Megrez 
at the junction of the handle with the 
bowl is the faintest of the seven. 
Benetnasch at the end of the handle is 
next in brightness to Megrez. Benet- 
nasch is a star of the Sirian type and 



OF THE SKY 81 

is so far away that its distance can- 
not be measured by the parallax 
method. By the revelation of the spec- 
troscope it is found to be coming 
towards the solar system at the rate 
of 16 miles per 'second. This star is 
about 25 degrees from Dubhe, one of 
the pointers. 

Dubhe the nearest pointer to the pole 
is a great spectroscopic binary, and is 
coming towards the earth at about 12 
miles per second. 

Merak the pointer farthest from the 
pole is a beautiful white star and is 
of the Sirian type. It is some 8 de- 
greed from Phecda, the other star at 
the bottom of the bowl. 

This very prominent and beautiful 
constellation Ursa Major, is also dis- 
tinguished because ot other noted ob- 
jects now to be mentioned. 

(1) Groombridge 1830, often called 
a "run-away" star, is traveling at a 
terrific speed, probably more than 200 
miles per second. It is a sixth magni- 
tude star, and therefore among the 
faintest to be seen with the naked eye. 
Yet it must be a very large sun, and 
at an enormous distance from us, 
for notwithstanding it's great velocity 
it would take 100 years for it to pass 



82 THE MATHEMATICS 

over a distance on the face of the sky 
equal to % that of the diameter of the 
moon. It cannot be less than 200 tril- 
lions of miles, or 34 light years from 
the 'sun. Its rate of motion is so ter- 
rific, that while it could be turned in- 
to a new direction by a near approach 
to a great sun, yet it could not be 
stopped except by collision with a body 
of enormous size. Its proper motion is 
7 seconds of a degree annually. 

(2) Planetary Nebula M. 97. Speak- 
ing in general terms of Nebulae, they 
are faint looking objects appearing as 
specks of luminous clouds. Only two 
can be seen with the naked eye, but 
10,000 of the irresolvable ones have 
been catalogued, and it has been es- 
timated that there are at least 120,000 
of them in reach of the great tele- 
scopes. Sir Wm. Herschel discovered' 
a large number of them. The spectro- 
scope shows that many of these lumin- 
ous clouds are gaseous in character, 
and not made up of separate or indi- 
vidual Suns. A large number of them 
lie relatively near the southern pole of 
the heavens. The Planetary Nebulae 
are nearly circular in form, and look 
much like the disks of the remoter 
planets of the solar system. 



OF THE SKY 83 

But back to the Planetary Nebula M. 
97 in Ursa Major. It is located in 
Right Ascension 11 h 9 m, and 55 de- 
grees 34 minutes Northern Declination. 
As viewed in a telescope of moderate 
size it ha's a faintly luminous disc near 
the size of Jupiter. But as viewed 
through more powerful glasses it ap- 
pears to be more complicated in char- 
acter. This great Nebula gives a 
spectrum of bright lines, which proves 
that it is gaseous. It has been cal- 
culated by astronomer's that if this 
Nebula was located at a distance of 
8 light years, or 48,000,000.000.000 miles 
from us, it would fill a space 7 times as 
great as the entire orbit of Neptune. 
But it is doubtless many times that 
distance, and cannot be seen without 
the ?id of the telescope. 

(3) Xi Ursae Major is. This very 
beautiful 4th magnitude star is found 
in Right Ascension 11 h 13 m, and 32 
degrees 6 minutes Northern Declina- 
tion. It is a fine binary, but the com- 
ponents being only 2 seconds of a 
degree apart, they do not show up well 
in small telescopes. They revolve 
around their common center of gravity 
in about 61 years. The "spectroscope 
shows that there is a third star in 



S4 THfi MATHEMATICS 

this great system, so that while there 
appears to be only one star to the 
naked eye, there are really three in 
the system. This was one of the first 
great binary 'systems to be recognized, 
and it is notable because of the fact 
that it was really the first double sys- 
tem whose orbit was calculated on the 
principles of universal gravitation. 



CHAPTER TWENTY-TWO 
CASSIOPEIA 

This very beautiful constellation is 
exactly on the opposite side of Polaris 
from the Big Dipper, and te about 30 
degrees from the pole. In all there are 
67 stars visible to the unaided eye, but 
if a great telescope should be turned on 
this constellation there would appear 
hundreds of thousands of great suns. 
It can be easily traced out because 
of the peculiar shape of its most 
prominent stars. The 7 most con- 
spicuous stars present the figure of a 
chair inverted, and according to the 
myth Cassiopeia is supposed to have 
occupied this chair as queen. Kappa 
on the front edge of the 'seat is only 
of the 4th magnitude and not so bright 
as the others. Schedir is the Alpha 
star of the constellation, and is a vari- 



OF THE SKY 85 

able with an irregular period. Caph 
the Beta star is white in color and of 
the second magnitude. It is situated 
on the equinoctial colure, and is on the 
same side of the pole as Polaris. 
Gamma the second star in the seat is 
at present considered the brightest in 
the constellation, although a few years 
ago Alpha was thought to be the 
brightest. Delta at the bend in the 
back of the chair is a second magni- 
tude star, while Epsilon at the top of 
the back is of the third magnitude. 

The other interesting objects in Cas- 
siopeia are the following: 

(1) The Eta star in Cassiopeia is 
one of the most interesting in the 
constellation. This star is located in 
Right Ascension Oh 43m, and 57 de- 
grees 17 minutes Northern Declina- 
tion. Look for it on some clear night. 
It will be found nearly between Alpha 
and Gamma, and about 2 degrees from 
the former. It is a great binary sys- 
tem of rapid motion and yields a large 
parallax. The components are yellow 
and purple in color, and are about 6 
seconds of a degree apart. A 3-inch 
telescope will show the components in 
good shape. This great system is about 
16 light years, or 96,000,000,000,000 



86 THE MAI HEMATICS 

miles from us. Suppose you try to 
count 96 trillians at the rate of one 
every second. In order to complete 
the task you would have to live 3,000,- 
000 years. The components of this sys- 
tem revolve around their common 
center of gravity in about 206 years. 
It has been calculated that the light- 
giving power of this double system is 
about equal to that of our sun, and 
that the mean distance between them is 
41 times that of the earth from the 
•sun. In other words they are 1,000,- 
000,000 miles further apart than the 
sun is from Neptune. 

(2) A Famous Temporary star ap- 
peared in Cassiopeia in the year 1572, 
not far from Kappa. It has been cal- 
led Tycho's star because it was care- 
fully observed and described by Tycho 
Brahe. When at its best it was bright 
enough to be easily seen in the broad 
light of day. These phenomena come 
into view with amazing suddenness and 
as unexpectedly. As this star out- 
shone the planet Jupiter it was much 
brighter than the first magnitude. 
There was no other star nearly so 
bright as this one when it burst forth 
on the evening of November 11, 1572. 
At first it increased in brightness till 



OF THE SKY S7 

it exceeded the planet Venus when 
shining at her best. But it finally be- 
gan to lose its light, changing to red- 
ness as it did so, and in 16 months, or 
in March, 1574, it became invisible, 
and has not been seen since. 

(3) Iota in Cassiopeia, located in 
Right Ascension 2 h 21 m, and 66 de- 
grees 57 minutes Northern Declination 
is a great triple system. It is a 5th 
magnitude star and in the Milky Way. 

Sigma in Cassopeia, located in Right 
Ascension 23 h 54 m, and 55 degrees 
12 minutes Northern Declination is a 
fine double 'star. It is of the 5th 
magnitude and situated a few degrees 
west of south from Beta. 

A small telescope, or even an opera- 
glass, will bring to view many beauti- 
ful regions in Cassiopeia, which can- 
not be seen with the naked eye. 

Near Sigma described above is a 
beautiful cluster of small stars dis- 
covered by Miss Caroline Herschel, 
sister of the great astronomer, Wm. 
Herschel. This leaas to the remark 
that the great and fascinating field of 
astronomy is open as wide to women 
as it is to men, and there are a number 
of women who have become distin- 
guished on account of their studies and 
researches in this noble science. 



88 THE MATHEMATICS 

Something like a degree from Delta 
at the bend of the chair's back will be 
found another fine Held of stars, if one 
will use a small glass. A person with 
a 3-inch telescope can spend a week 
or a month with great pleasure and 
profit in observing and studying the 
beautiful objects in and around Cassio- 
peia. 



CHAPTER TWENTY-THREE 

THE GREAT NEBULA IN 
ANDROMEDA 

The constellation Andromeda is 
more than 30 degrees in length, and its 
main stars together with those of the 
Great Square o<f Pegasus suggest to 
some the outline of an immense dipper. 
While it is not at all comparable with 
the Big Dipper previously discussed, 
yet the enthusiastic and industrious 
searcher of the heavens will have no 
trouble in locating it. Find the Pleiades, 
look to the northwest about 35 degrees, 
and your eyes will be in the borders 
of Andromeda. 

As we are now to consider briefly 
Andromeda's Great Nebula, it will be 
well at this time to locate it. You 
will find it in Right Ascension Oh 



OF THE SKY 89 

37 m, and 40 degrees 43 minutes 
Northern Declination. It is about 20 
degrees almost due south from Cassio- 
peia's chair. As stated in Chapter 
Twenty-one, there are estimated to be 
at least 120,000 Nebulae in the entire 
heavens, but only two can be seen with 
the unaided eye. Andromeda's Nebula 
is one of the naked-eye objects. 

In order to keep up with Andromeda 
and the Nebula, observe the following, 
remembering that this constellation is 
north of the celestial equator and also 
of the ecliptic. It therefore rises and 
sets north of the rising and setting sun. 

About January 1, at 7 P. M., Andro- 
meda lies just west of the meridian, 
February 1, at 7 P. M., it is 30 de- 
grees further west; March 1, at 7 P. 
M., it is approaching the western hori- 
zon; April 1, at 7 P. M., it is just 
setting in the northwest; during May, 
June, and July, it is invisible in the 
evening sky, but August 1, at 9 P. M., 
it can be seen above the horizon in 
the northeast; September 1, at 8 P. M. 
it is advancing towards the meridian ; 
October 1, at 7 P. M. it is nearly 
midway to the zenith; November 1, at 
7 P. M., it is east of the meridian ; 
December 1, at 7 P. M. it is almost 
on the meridian. 



90 THE MATHEMATICS 

As to the Great Nebula in Andro- 
meda, it is sometimes called "The 
Queen of the Nebulae." It is clearly 
seen on a moonless night, resembling 1 
a small cloud. In a 3-inch telescope it 
is large and round, but in larger glasses 
it appears elliptical. It is calculated to 
'be 3% degrees in length, or fully 30,000 
times the distance of the earth from 
the sun. 

From the latest photographs of this 
Nebula, made with large telescopes, it 
appears to be spiral in form, and may 
in future ages develop into a great 
solar system. 

The Temporary star of 1885 blazed 
out very suddenly near the center of 
the Nebula, continuing visible for about 
6 months, and then faded out of 
sight till the most powerful telescopes 
were unable to reach it. It is fully 
believed that this star was actually in 
the Nebula, that is, that there was a 
real connection between the Nebula 
and the star. 

Gamma in Andromeda, a third mag- 
nitude star about 16 degrees west of 
Algol, is one of the finest double stars 
to be found in the sky. The compo- 
nents are yellow and blue. The smaller 
one is itself a binary with a period of 
55 years, and the eccentricity of its 



OF THE SKY 91 

orbit is very great. It is really a great 
system of three stars, though appar- 
ently only one. 



CHAPTER TWENTY-FOUR 
OTHER GREAT NEBULAS 

Of the thousands of other Nebulous 
objects in the Sky, we can consider 
only a few of the most prominent. 

(1) The Great Nebula in Orion. 
This is one of the most noted of the 
large and irregular Nebulas, and is 
situated in Right Ascension 5 h 30 m, 
and 5 degrees 27 minutes Southern 
Declination. It is in one of the finest 
constellations in the entire heaven's. 
In Chapter Sixteen we considered Rigel 
which is the great electric sun of this 
constellation. This Nebula surrounds 
the noted multiple star, Theta. It is 
strange that Galileo, who invented and 
used the first real telescope and gave 
much attention to the beautiful object's 
in Orion, overlooked this great Ne- 
bula. While this Nebula appears to 
the naked eye as one object, a 3-inch 
telescope shows that there are four 
stars, which are of the fifth, sixth, 
seventh and eighth magnitudes. They 
form what astronomers call the tra- 



92 THE MATHEMATICS 

pezium of Orion. More powerful tele- 
scopes show two additional stars, mak- 
ing six in the trapezium. There are 
really many more smaller stars. 

This Nebula is undoubtedly composed 
of luminous gas, and is not simply 
a cluster of small stars irresolvable in 
the great telescopes. Until some 60 
years ago, astronomers supposed all 
the Nebulas of the sky to be ir- 
resolvable cluster's of stars, but the 
wonderful spectroscope during the past 
half century has revealed the fact that 
a large number of these objects are 
composed of true gases. From later 
observations of this Nebula, it ap- 
pears that the star's of the trapezium 
are not only optically connected with 
the Nebula, but are physically related 
to it, and are probably condensed from 
the gaseous matter ot the Nebula. The 
light of this great Nebula comes from 
the luminous gas, hydrogen, and helium 
and the gas hitherto undetected upon 
earth which has been called Nebulum. 
We also learn from the spectroscope 
that this great Nebula is composed of 
the same elements as the stars of that 
constellation. It is without doubt as 
remote as are the stars about it, the 
distance being immeasurable, and it is 
getting further away from the solar 



OF THE SKY 9} 

system at the rate of 10 miles per sec- 
ond, or 315,360,000 miles each year. 
Some believe that this great Nebula is 
at least 1000 light years from us, and if 
so, it will take 19,000 years for it to 
add another light year to its present 
distance. 

(2) Eta in the constellation Argo is 
surrounded by a very magnificent Ne- 
bula. In appearance it is very much 
like the Great Nebula in Orion. It is 
in Right Ascension 10 h 41 m, and 59 
degrees 10 minutes Southern Declina- 
tion. It is a little less than 31 degrees 
from the south celestial pole, and 
therefore too far south to be observed 
in the United States. But the study of 
it is full of interest. It is situated in 
a very magnificent portion of the Milky 
Way. The most powerful telescopes 
are unable to resolve any part of it 
into stars, and it seems to be composed 
entirely of luminous gas. There are 
many stars scattered over it, and some 
of these may be physically connected 
with it. It is of vast extent, covering 
apparently a space about five times the 
area of the full moon, and therefore 
it must have vast dimensions. 

The Eta star in Argo is one of the 
most remarkable stars in the sky, and 
appears near the middle of the Nebula 



S>4 THE MATHEMATICS 

just described above. It is a variable 
star, and the history of its changes is 
full of interest. From the time of 
Halley's observations of it in 1677 to 
1837 it was a naked-eye star ranging 
between the 2d and 4th magnitudes. 
But in 1837 it rapidly increased in 
brightness and became 1st magnitude, 
decreased somewhat in brightness 
again, and in the year 1843 it became 
almost as bright as Sirius. For several 
years following it gradually lost its 
brightness till it reached the 7th magni- 
tude where it remains. 

(3) The Great Spiral Nebula in 
Canes Venatici. This Nebula was ob- 
served and studied by Lord Ros k se in 
his great telescope at Parsonstown, 
Ireland. It is the most noted of all 
the spiral Nebula, situated in Right 
Ascension 13 h 26 m, and 47 degrees 
42 minutes Northern Declination, about 
3 degrees southwe'st of Benetnasch, the 
star at the end of the Big Dipper's 
handle. This Nebula was discovered 
by Messier while he was engaged in 
hunting comets on October 13, 1773. 
The smaller telescopes show two Ne- 
bulas almost in contact, one 'smaller 
than the other, but in the more power- 
ful glasses it appears as a wonderful 
spiral. 



OF THE SKY <o 

From the latest photographic work 
it has been shown that a considerable 
proportion of the Nebulas are spiral 
in form, and this form is now con- 
sidered the rule, contrary to earlier 
opinions concerning Nebulas. 

(4) The Ring Nebula in Lyra. This 
beautiful Nebula as it appears in the 
telescope is easy to find. It is in Right 
Ascension 18 h 50 m, and 32 degrees 
54 minutes Northern Declination. It 
is near Beta in Lyra and about one- 
third the distance from Beta to Gam- 
ma, and about 10 degrees southeast 
from Vega. It can be seen in a low 
power telescope. The great Lick Ob- 
servatory has given a very fine photo- 
graph of it. This is regarded as the 
most noted, and is thought to be pos- 
sibly the nearest to us of the ring 
Nebulas. Only one bright line is 
shown in the spectrum. While Lord 
Rosse and other astronomers thought 
it could be resolved into stars, none 
are perceptible in the great telescopes 
of this country, and with the use of 
the spectroscope it is found by Huggins 
to be of a gaseous nature. Barnard 
found the central star in it to be in- 
conspicuous and of the 15th magnitude. 
It is found to be about 81 seconds of 
an arc in length by 59 seconds of 



96 THE MATHEMATICS 

arc in width, or double the apparent 
area of the disk of Jupiter. While 
little is known of its real size and 
distance, it seems evident that if the 
entire solar system should be placed 
in its center it would all occupy no 
more space than that covered by the 
central star. Enormous then must be 
its distance and vast the real size of 
this Nebula. 

The great telescopes with the use of 
the photographic plates have brought 
to view 4,800 stars on and near the 
Nebula covering an area of 3 square 
degree's. 



CHAPTER TWENTY-FIVE 
SOME GREAT STAR CLUSTERS 

In Chapter Nine we studied the 
Pleiades, or the Seven Stars. This as 
well as a few others can be seen with 
the naked eye. A number of others 
can be found with small telescopes. 

(1) The Great G\lobular Cluster in 
Hercules. Thi k s cluster is found in 
Right Ascension 16 h 38 m, and 36 
degrees 37 minutes Northern Declina- 
tion. It is one of the most remark- 
able clusters in the heavens, and one 
of the finest for observation in the 
telescope. It is known as Messier 13 



OF THE SKY 97 

because it is No. 13 in Messier's cata- 
logue. It is found on the star maps 
not far from the Apex of the sun's 
way, and between Zeta and Eta in 
Hercules. It is about 28 degrees near- 
ly west of Vega. It appears as a hazy 
star of about the 6th magnitude in 
a good opera-glass. This beautiful 
and wonderful cluster was discovered 
by Halley in the year 1714, and when 
Messier observed it in a glass of low 
power, he thought it contained no stars. 
But when a great telescope is turned 
on the cluster it is found to contain 
a multitude of stars, which can be 
seen and counted. Observers through 
the Harvard telescope have counted 
724 stars outside of the Nucleus. 
While the entire cluster contains at 
least 5,000 stars, Sir Wm. Herschel 
believed it contained as many as 14,000. 
Remember that a person with good 
strong eyes can 'see tne cluster without 
the aid of a telescope. In a 3-inch 
telescope it is indeed a beautiful ob- 
ject, a number of its outlying stars 
being discerned. Some astronomers 
have estimated this great cluster to be 
558 billions of mile's in diameter, and 
the distance to be 65 light years from 
us, or 390 trillions of miles. 



98 THE MATHEMATICS 

(2) Cluster 92 Messier in Hercules. 
This cluster is only a few degrees 
Northeast of the one just described 
above. It is between Eta and Iota, 
and about 50 degrees west of Deneb 
the great sun in Cygnus which was 
discussed in Chapter Fifteen. It is 
located in Right Ascension 17 h 14 m, 
and 43 degrees 15 minutes Northern 
Declination. While the brighter stars 
of this cluster are easily reached by 
small telescopes, the cluster as a whole 
is not so bright nor so easily resolvable 
into stars as the cluster we have just 
been considering above. Wm. Her'schel 
found it to be nearly 8 minutes of an 
arc in diameter, but its distance from 
the solar system is so vast that its 
real dimensions have never been es- 
timated. Lord Rosse's great 6-ft. re- 
flecting telescope was unable to resolve 
the central part into stars. 

(3) Globular Cluster Omega Centauri, 
Sir John Herschel when studying this 
great cluster in a powerful telescope 
spoke of it as the richest and largest 
object of its kind in the heavens, and 
he declares the stars are literally in- 
numerable and of the 13th and 15th 
magnitudes. 

We now transfer Irom the Northern 
to the Southern Heavens. There are 



OF THE SKY 99 

some very fine globular clusters in the 
Southern Hemisphere, but probably 
none will exceed in magnificence the 
one now under consideration. It is 
located in Right Ascension 13 h 21 m, 
and 46 degrees 47 minutes Southern 
Declination. It is about 25 degrees 
southwest of Alpha Centauri previously 
"studied, and about the same distance 
from Alpha Crucis. A few years 
ago this great cluster was photographed 
with a 13-inch telescope, and the in- 
dividual stars can De distinctly seen 
and counted. While the telescope shows 
at least 6,500 stars in the cluster, it is 
believed that the real number is much 
greater. The dimensions of this cluster 
measure about 20 minutes of an arc, 
which is nearly % the apparent dia- 
meter of the moon. To the unaided 
eye it has the appearance of a hazy 
comet, and is said to give as much 
light as a 4th magnitude star. This 
cluster has 125 variable stars, 98 of 
them having short periods of less than 
24 hours. 



100 THE MATHEMATICS 

CHAPTER TWENTY-SIX 

THE STUPENDOUS VOYAGE OF 
THE SOLAR SYSTEM 

It will be well right here to turn 
back and read Chapter Eight. There it 
was found that the sun and his family 
are actually in motion, speeding 
through space at a rapid rate, covering 
about 350,000,000 miles annually, and 
that since the days of Adam the solar 
system has covered only 2,100,000,000,000 
miles, or about one-twelfth the distance 
to the nearest star. 

Since the invention of the telescope 
and the spectroscope, the direction in 
which the sun and his family are 
traveling has been found. The great 
astronomer, Wm. Herschel, was the 
first to make investigation on this very 
interesting and important question. It 
was in 1783, or 137 years ago that he 
began to study this subject. As a result 
of the study of the proper motion of 
stars as related to this theme, he ar- 
rived at the conclusion that the solar 
system is in rapid motion, traveling in 
the direction of the constellation Her- 
cules, and the particular point toward 
which it is tending is located near the 
star Lambda in Hercules. This is 
near Right Ascension 17h 30m, and 



OF THE SKY 101 

36 degrees Northern Declination. This 
can be easily located on a good star 
map. It is something like 20 degrees 
southwest of the brilliant star Vega 
studied in Chapter Ten. This point 
towards which the sun is tending is 
called the Apex of the sun's way. The 
point opposite to this in the heavens, 
or that point from which the sun and 
his family are traveling is almost mid- 
way between the two great southern 
suns, Sirius and Canopus, discussed in 
Chapters Ten and Twelve. It is about 
18 degrees nearly due south of Sirius. 
A little later, other astronomers as 
the result of their study of the sub- 
ject, calculated that the point towards 
which the sun is traveling is about 10 
degrees north of the point calculated 
by Herschel, or about 17 degrees a 
little south of west of Vega. A num- 
ber of astronomers have since studied 
this question and w T hile the results 
found by different ones vary to some 
extent, it is wonderful how nearly they 
all agree in locating the Apex of the 
sun's w r ay. Newcomb is among the 
later ones who have given much study 
to this subject, and as a result of his 
studies the Apex of the sun's way, or 
the point toward which the solar sys- 
tem is traveling is placed near the 



102 THE MATHEMATICS 

borders of Hercules and Lyra, not far 
from Righ Ascension 18 h 30 m, and 
35 degrees Northern Declination. This 
point is about 6 degrees southwest of 
Vega or something like 12 degrees 
northeast of the point fixed by Her- 
schel. 

The present trend, therefore, of the 
solar system is nearly towards Vega, 
and we learned in Chapter Ten that 
the relative rate of approach of the 
sun and Vega is about 11 miles per 
second and that at this rate it will 
take the sun 558,000 years to pass by 
Vega. 
A k s the sun is traveling nearly towards 
Vega at the rate of 11 miles per sec- 
ond, or about 350,000,000 miles each 
year, it is evident that the stars in 
that quarter should open out from each 
other, and those in the opposite part 
of the heavens should close up behind, 
while those in the section of the 
heavens between should on the whole 
drift backwards, and this is exactly 
what is happening. We have many 
illustrations of this on the earth. For 
example, if we approach a grove of 
trees, they will seem to become larger 
and the spaces between them to open 
out, while those in the fear will seem 
to become smaller and to close up. 



OF THE SKY 103 

Sometimes it is asked, "How can 
the sun go forward carrying with him 
the 8 large planets, 600 asteroids, 2'd 
moons, and a number of comets, and 
they all maintain their proper rela- 
tions to him, seeing that the planets 
have their own motions around the 
sun, and the moons their motions 
around their respective planets" ? 
Probably we can get some idea of this 
by using a familiar illustration. We 
are on a passenger train traveling 
forward at the rate of 50 miles an 
hour. While the car is in full speed 
a person walks from the rear to the 
front part of the car, and while do- 
ing so a fly fixes itself on his face. 
He brushes it off, and it flies around 
his head a number of times while he 
is walking through the car. The pas- 
sengers who are seated have only one 
motion — that of the car. The person 
who walks through the car while it is 
in motion has two motions — that of 
the car and his own motion while he 
is walking. The fly has three motions 
— that of the car, that of the person 
who is walking through the car, and 
its own motion while flying. Not- 
withstanding all are on the same train, 
while the person walks forward he is 
traveling more rapidly than those who 



104 THE MATHEMATICS 

remain seated, for he has the motion 
of the car, 50 miles per hour, plus his 
own motion while walking. 

But it is believed that the solar sys- 
tem is moving in a curved path and 
not in a straight line, but so far as 
actual observations allow us to speak, 
we can only say that he has yet 
passed over a very small part of his 
mighty orbit. The sun will probably 
travel for hundreds or even thousands 
of years, before it will seem to deviate 
from a straight course. Whether it is 
traveling in a straight or curved path, 
it is certainly on a tremendous journey. 
If it is moving in a curved path, is 
this path an orbit, and will it there- 
fore finally finish a revolution and in 
future ages come around to the posi- 
tion it now occupies in space? These 
are some questions not yet solved by 
astronomers. 

The fascinating idea that somewhere 
in space there exists a great central 
star or sun, around which all the stars 
revolve, has had its advocates. It is 
a very beautiful theory, but few astro- 
nomers are inclined to put much con- 
fidence in it. 

About 70 years ago, Maedler, a Ger- 
man astronomer, in one of his astro- 
nomical works took the position that 



OF THE SKY 105 

the entire stellar universe revolves 
around the center of gravity of the 
whole, and that Alcyone, the brighest 
star in the Pleiades, is the great central 
sun of the universe. Since then, 
others have advocated this theory, 
among them Andre in a published work 
on Stellar Astronomy. He argues the 
idea of a great central sun, contending 
that it agrees with many facts per- 
taining to the proper motion of stars. 
According to his published account of 
the matter, the solar system is distant 
from Alcyone about 4290 trillions of 
miles and will complete a revolution 
around that star in about 22,000,000 
years. 



CHAPTER TWENTY-SEVEN 

THE PENETRATING POWER OF 
TELESCOPES 

We are now entering another great 
subject, the telescope and its millions 
of lessons. I say millions of lessons, 
for that is true. Every star or sun, 
or other object in tfte heavens, invis- 
ible to the naked eye, but brought to 
view by means of the telescope, is 
really a new revelation, an added les- 
son to what we already know. The 



1 6 THE MATHEMATICS 

human eye is a great scientific instru- 
ment, built by THE GREAT SCIEN- 
TIST, the Author of the Universe. 
It is wonderful how many things can 
be seen with the unaided eye. Refer- 
ence is made to the human eye in the 
following passage of Scripture, (Gen. 
15 : 5) : "Look now towards heaven 
and tell the stars, if thou be able to 
number them, so shall thy seed be." 
Also the following: ''Lift up your eyes 
on high, and behold who created these 
things, that brought out their host by 
number: He calleth them all by names 
by the greatness of His might, for that 
He is strong in power, not one fail- 
eth." (Isa. 40:26). 

A very 'small per cent of the differ- 
ent objects that make up the universe 
can be seen with the naked eye. By 
far the larger number of objects com- 
posing the solar system must be seen, 
if seen at all, by means of the tele- 
scope. We can see the sun, Mercury, 
Venus, Mar's, Jupiter, Saturn, our 
Moon, and under favorable conditions 
probably Uranus, with the naked eye. 
But Neptune, the 600 asteroids, 'Mars' 
two moons, Jupiter's eight, Saturn's 
ten, Uranus' four, and Neptune r s one 
(making a total of 25 moons) are all 
invisible without telescopic aid. A 



OF THE SKY 107 

good strong eye can see distinctly up- 
wards of 6000 stars in the entire heav- 
ens. This takes in all the stars down 
to and including the 6th magnitude. 
If one should look through a good 
opera-glass he would see stars of the 
7th magnitude, and of these there are 
13,000 in all. All the stars of the first 
seven magnitudes bring the number to 
about 20,000. A small astronomical 
objective glass, but a little more power- 
ful than an opera-glass, penetrates to 
the 8th magnitude of stars, of which 
there are about 40,000. Now when we 
add together all the stars of the first 
8 magnitudes we have 60,000 stars. 

The light-gathering power of tele- 
scopes depends on the area of their 
object-glasses, and the amount of light 
collected is proportional to the square 
of the diameters of their object-glasses. 
The pupil of the human eye is about 
one-fifth of an inch in diameter. That 
being true, a 1-inch telescope will col- 
lect 25 times as mucn light from a star 
as the naked eye receives. It will there- 
fore penetrate farther out into space 
and reach stars that cannot be reached 
by the unaided eye. 

If you look through a 1— inch tele- 
scope, you will sec stars of the 9th 
magnitude, and there are 120.000 of 



108 THE MATHEMATICS 

these. Putting together all the stars of 
the first 9 magnitudes, we have about 
180,000. 

i\ext suppose you study the heavens 
through a telescope with an object-glass 
of 2 inches in diameter. On the prin- 
ciple stated above, the 2-inch glass 
receives 100 times as much light as 
the naked eye, and brings to view 10th 
magnitude stars, of which there are 
380,000. Adding these to the total 
above mentioned we have 560,000 stars 
of the first 10 magnitudes. 

Try next a telescope with a 3-inch 
object-glass. This telescope receives 
225 times as much light as the naked 
eye, and penetrates farther out into 
space bringing to view stars of the 
11th magnitude. Of the 11th magni- 
tude stars there are 1,000,000, making 
a total of 1,560,000 stars of the first 11 
magnitudes. A 4-inch telescope will 
enable one to look at stars of the 12th 
magnitude of which there are 3,000,000. 
This makes 4,560,000 stars of the first 
12 magnitudes, and the 4-inch glass 
receives 400 times as much light as 
the naked eye. 

That part of the universe thu's far 
found has begun to take on some dimen- 
sions. We now wish to introduce the 
7-inch telescope, which is capable of 



OF THE SKY 109 

receiving 1225 times as much light as 
the unaided eye, and by its penetrating 
power it reaches stars of the 13th 
magnitude, of which there are 9,000,- 
000. This makes a grand total of 13,- 
560,000 'stars of the first 13 magnitudes. 
If one should undertake to count all 
these stars it would require more than 
5 months, counting une star every sec- 
ond, night and day. 

To those who may have a curiosity 
to look through the largest telscopes, 
we would like to say that they will 
find the moderate glasses more satis- 
factory. And they should also re- 
member that a large proportion of the 
astronomical discoveries have been 
made with relatively small glasses, and 
very much of the solid astronomical 
work of the present time is carried on 
with meridian circle's which have 
glasses ranging from 4 to 8 inches in 
diameter. 

Sir Wm. Herschel discovered the 
planet Uranus and many hundreds of 
beautiful Nebulas with a small glass. 
The 4 larger moons of Jupiter, the 
rings of Saturn and the mountains and 
craters of the moon were discovered 
with a ^mall glass. W. S. Burnham. 
an enthusiastic and industrious astro- 
nomer of Chicago made himself famous 



110 THE MATHEMATICS 

by the use of a 6-inch telescope. He 
purchased his instrument from Clark 
and Son of Cambridge, Mass., and 
discovered many hundreds of double 
star's so difficult that they had escaped 
the attention of those using larger 
glasses. On Mount Hamilton, Cali- 
fornia, afterwards the site of the 
great Lick telescope, he discovered 
nearly 50 new double stars, all of 
which were unknown to previous ob- 
servers, using his 6-inch telescope. 

Let us next introduce the 10-inch 
telescope. This instrument receives 
2500 times as much light as the naked 
eye, and its penetrating power is so 
vast that it reaches 'stars of the 14th 
magnitude, of which there are 27,000,- 
000. These with the former total bring 
the number of stars of the first 14 
magnitudes to upwards of 40,000,000. 
It would require one year and three 
months to count these, counting one 
every second night and day. 

In order to reach stars of the 15th, 
16th and 17th magnitudes, it requires 
the largest telescopes. The great Yerkes 
glass with 40 inches aperture barely 
brings to view stars of the 17th magni- 
tude. The penetrating power of this 
glass is enormous. It receives 40,000 



OF THE SKY ill 

times as much light as the naked eye, 
and reenforced by celestial photo- 
graphy, it brings to view not less than 
100,000,000 shining suns. In order to 
count them one must spend 3 years 
and 2 months, counting night and day, 
one every second. 



ERRATA 

On page 25, third line from the top, 
read part for par. 

On page 29, sixteenth line from top, 
read Southern instead of southern. 

Doubtless a few other typographical 
errors will be found. 



